{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The comet 67P/Churyumov–Gerasimenko\n",
    "\n",
    "This tutorial teaches you how to use the IAS15 integrator (Rein and Spiegel, 2015) to simulate the orbit of 67P/Churyumov–Gerasimenko. We will download the data from NASA Horizons and visualize the orbit using matplotlib.\n",
    "\n",
    "This tutorial assumes that you have already installed REBOUND."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NASA Horizons**\n",
    "\n",
    "If you're interested in Solar System dynamics, you have probably heard of NASA Horizons. It's a large database of Solar System objects, their orbits and physical properties. It includes planets, moons, satellites, asteroids, comets and spacecrafts. With REBOUND, you can easily import data from NASA Horizons. As an example, let's pull in the present day positions of Jupiter, Saturn and the Sun:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Searching NASA Horizons for 'Sun'... \n",
      "Found: Sun (10) \n",
      "Searching NASA Horizons for 'Jupiter'... \n",
      "Found: Jupiter Barycenter (5) (chosen from query 'Jupiter')\n",
      "Searching NASA Horizons for 'Saturn'... \n",
      "Found: Saturn Barycenter (6) (chosen from query 'Saturn')\n"
     ]
    }
   ],
   "source": [
    "import rebound\n",
    "sim = rebound.Simulation()\n",
    "sim.add(\"Sun\")\n",
    "sim.add(\"Jupiter\")\n",
    "sim.add(\"Saturn\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now all the data is in REBOUND! Let's have a look at the orbits of the two planets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<rebound.Orbit instance, a=5.202605226783334 e=0.04835899225976217 inc=0.022751635168853 Omega=1.7543795407720049 omega=4.772560939899953 f=6.184996339543184>\n",
      "<rebound.Orbit instance, a=9.544614098295511 e=0.054806111930824235 inc=0.04341725686895089 Omega=1.982680560323928 omega=5.904608872970777 f=4.061882597282457>\n"
     ]
    }
   ],
   "source": [
    "for orbit in sim.orbits():\n",
    "    print(orbit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although there are three bodies, the `orbits()` function only returns two objects as the orbit for the Sun would be a little boring. The function returns the orbits in Jacobi coordinates. Since we didn't specify a value for $G$, REBOUND assumes that $G=1$. The unit of length is one astronomical unit, the unit of time is one year/$2\\pi$.\n",
    "\n",
    "Let's add something more interesting to our simulation: the comet 67P/Churyumov-Gerasimenko. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Searching NASA Horizons for 'Churyumov-Gerasimenko'... \n",
      "Found: 67P/Churyumov-Gerasimenko (chosen from query 'Churyumov-Gerasimenko')\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rein/git/rebound/rebound/horizons.py:165: RuntimeWarning: Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\n",
      "  warnings.warn(\"Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\", RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "sim.add(\"Churyumov-Gerasimenko\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When searching for a body by name, REBOUND takes the first dataset that Horizons offers. In this case, it's a set of parameters from 1962. You probably want to go to the Horizons website and check that the values you are using are up-to-date and appropriate for what you want to do. You can also use more complicated Horizons queries, for example, to get the most recent apparition solution for the comet, use\n",
    "\n",
    "    sim.add(\"NAME=Churyumov-Gerasimenko; CAP\")\n",
    "\n",
    "You can also use the IAU asteroid number for numbered asteroids, or the database record numbers from Horizons for objects not yet numbered by the IAU (but note that database record numbers can change as the database gets rearranged with new discoveries, see https://ssd.jpl.nasa.gov/?horizons_doc#sb for details). In our case the current database record number is 900647, so you could use `sim.add(\"900647\")` to get the newest set of orbital parameters for Churyumov-Gerasimenko.\n",
    "\n",
    "NASA Horizons doesn't have masses for all bodies. If REBOUND doesn't find a mass, you get a warning message (see above). In our case, we don't need the mass of the comet (it's really small). However, it you want, you can add it manually using the syntax `sim.add(\"Churyumov-Gerasimenko\", m=5.03e-18)`.\n",
    "\n",
    "Before we integrate the orbits, let's plot the instantaneous orbits using the built-in REBOUND class `OrbitPlot`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QICoqyjoCbWxsZB2J96g8SZfT6/XYvn07dDodZs6ciYCAANaRCHE4rQXq7u6OnJwcKlDGqDxJlzIajdi5cyfq6+vx4IMP0jUMCekAoVCI6Ohoa4HSLFx2qDxJlzGbzfj222+hVqsxbdo0+Pn5sY5EiMNrLVA3NzdkZ2ejubmZdSReovIkXcJisWDPnj0oKirC1KlT6RgnIZ2odRKRm5sb8vLyaCUiBqg8SZf45ZdfUFRUhIceegjh4eGs4xDidFpHoGKxGLm5uTAajawj8QqVJ+l0J0+exOnTpzFy5EhER0ezjkOI0xKJRNZ/Y7m5uTCbzYwT8QeVJ+lU2dnZ+OWXX5CcnIwBAwawjkOI0xOLxYiOjobBYMDVq1fBcRzrSLxA5Uk6TXl5Ob7//nv06tULd911F+s4hPCGTCZDVFQUmpqaUFRUxDoOL1B5kk7R0NCAnTt3ws/PD1OmTIFAIGAdiRBecXd3R3h4OGpra1FZWck6jtOji2GTDtPr9di5cydcXFzw8MMPw8WF3laEsODl5QWdToeysjLIZDIolUrWkZwWjTxJh3Ach71790Kj0WD69Olwc3NjHYkQXgsMDIRSqURhYSH0ej3rOE6LypN0yG+//Ybz589jypQp8PX1ZR2HEAIgLCwMLi4uyM/Ph8ViYR3HKVF5ktuWm5uLI0eOYNSoUXRKCiF2RCQSISIiAkajEYWFhazjOCUqT3Jb6uvr8f333yMmJgYjRoxgHYcQ8gcymQxhYWFoaGhARUUF6zhOx6nKc82aNRAIBNfdevXqxTqW0zGZTNi1axekUinNrCXEjimVSgQEBKCqqooWke9kTjctsk+fPjhw4ID1a5r52fkOHz6M+vp6PPLII3B1dWUdh/wJjuNgMBhgNpthMplgsVjaXIlGKBRCJBJZb2KxGCKRiEFi0pkCAgKg1WpRVFSE2NhY2iZ2Eqd7FV1cXOh6kV0oJycHx48fx8SJExEYGMg6Dvk/BoMBzc3N0Gq1aGlpgU6ng16vh8FgsK55KhKJrKvPtO6Z+T2h8H87olofFwqFkEgkkEgkkMlkkEqlkMlk1hvtdXAMISEhyMnJQXFxMSIiIljHcQpOV545OTkICgqCTCZDcnIy1q1bh9DQ0Jt+v16vv246t0aj6Y6YDqm5uRl79uxBdHQ0hgwZwjoOb5lMJjQ0NKChoQGNjY1obGyEwWCwjhJdXV3h6uoKpVIJqVRqLb/WkWTr7Y8sFot1VGoymWAymWA0Gq0FrNVqUVdXB7PZDKFQCKFQCFdXV8jlcri5uUEul0Mmk3X3y0HaQSwWIyQkBPn5+aiurqaZ8Z3AqcozKSkJW7ZsQc+ePVFeXo6XX34ZI0aMwIULF6BQKNr8M+vWrcPLL7/czUkdD8dx+O9//wuLxYLJkyfTiKMbWSwW1NXVoa6uDrW1tWhsbATHcZDJZFAoFAgKCoJCoYCbmxtcXV27/O/GZDKhpaUFLS0t0Gq10Gg0qKqqgkAggEQigbu7O5RKJRQKBe0itCMKhQK+vr4oLy+3vlfI7RNwTryKcH19PcLCwrBhwwYsWLCgze9pa+QZEhKChoYGWp3jd86ePYs9e/Zg2rRp6N27N+s4Ts9kMqGqqgpVVVWorq6GyWSCXC6Hp6cnvLy84OXlBblczjqmlclkglarRVNTk3UkzHEc3NzcoFQqraNgwhbHccjJyYFQKERkZOR1u+rJte2/h4dHu7b/Tv2x0NPTE7GxscjNzb3p90ilUvpH/Sdqa2vx008/YcCAAVScXchisaC6uhplZWWorKyEUCiEu7s7wsLC4Ofnd9O9J/bAxcXFWpLAtTLVaDTQaDSoqKhAeXm5tfw9PT1pRMqIQCBAWFgYcnNzUVVVBX9/f9aRHJZTv4ObmpqQl5eH2bNns47isMxmM77//nu4ubnhnnvuYR3HKbXOhFSr1WhpaYFCoUBMTAwCAgIcdteai4sLvL294e3tDYvFgsbGRjQ0NECtVqOiogIeHh7w9vam5RwZkEql8PPzg1qthlKpdNj3GGtOVZ7PPfccJk2ahLCwMJSVlWH16tUQiUSYMWMG62gOKy0tDbW1tXj44YdphN7JqqurkZ+fj6qqKojFYvTo0QMhISF2PcK8HUKhEB4eHvDw8IDZbEZDQwPq6+tRWFgIiUQCb29veHp60i7EbuTr6wuNRoPS0lJERUXRHIbb4FTlWVJSghkzZqCmpgYqlQrDhw/HiRMnoFKpWEdzSPX19Th06BAGDhyIsLAw1nGcAsdxKC8vR25uLrRaLRQKBeLj4xEYGMiLcypFIpF1RKrValFbWwu1Wo2amhrr8Vzapdv1BAIBevTogby8PFRVVcHPz491JIfjVO/SHTt2sI7gNDiOw48//ghXV1eMGTOGdRyHx3EcSkpKkJubi+bmZqhUKvTp0wc+Pj6sozEjl8shl8thMplQW1trnU3cWq58+DDBkkwmg0qlQlVVFZRKJZ1mZCOnKk/SebKyspCdnY0ZM2bQ7toOqqysRFZWFjQaDYKCgjBw4EB4eHiwjmU3XFxc4OfnBx8fH9TV1aG+vh4NDQ3w9vaGl5cX7VLsQiqVCg0NDSgtLUVkZCS91jag8iQ30Ol02Lt3L3r16kVrA3dAQ0MDsrKyUFVVBR8fH4wYMQJeXl6sY9ktkUgEX19feHl5oaamBjU1Naivr4ePjw992OgirbtvCwoKUF9fT+9PG1B5khv8+uuvMBgMuPfee1lHcUhGoxGXL1/G1atX4eHhgaSkJDolwAYikQh+fn7w8vJCdXU1qqqqoNFo4OfnR3tBukDrKUSVlZVQKpW0u7ydqDzJddRqNY4fP44JEybQIhG3obS0FOfPn4fRaERcXByioqJoFultEovFCAwMhE6nQ2VlJUpKSuDp6Qlvb2/avdjJ/Pz8oNFoUFlZSWtWtxOVJ7nOvn374O3tjcTERNZRHIrBYEBGRgZKSkoQHByMfv360flznUQmk1lX/aqrq4NWq6VRaCdrPe5cUVEBLy8vmjzUDvSRmFhlZ2cjNzcX48ePp103NqioqMCBAwegVqsxZMgQJCYmUnF2MoFAAE9PTwQHB0MoFKK0tBS1tbVw4tVFu52XlxekUildOLudaORJAFxbGm7fvn2IiIigSULtZLFYcO7cORQVFcHX1xcDBw6kT+xdTCwWIygoyDoKbWlpgZ+fH8RiMetoDk8gECAgIACFhYVoaGigSVp/gsqTAABOnz6N6upqTJ06lY4ntUNzczNOnDiBhoYGxMfHIzo6mnUk3mgdhcrlclRVVaG8vBw+Pj601F8ncHNzg0KhQHV1NZRKJW0LboF22xLodDocPHgQAwYMoMkC7aBWq3H06FEYDAaMHj2aipMRiUSCwMBAuLq6Wk9rIR3n7+8Po9FIr+efoJEnQWpqKiQSCcaOHcs6it3Lzc3F2bNn4efnh+TkZEgkEtaReE0oFEKlUkGj0aC+vh5GoxG+vr40YuoAiUQCDw8P1NTUwMPDg2aL3wS9Kjyn1Wpx9OhR9O3b1+kWJO9MHMfhzJkzOHPmDGJiYnDnnXdScdoRpVIJlUoFvV6PiooKmEwm1pEcmq+vL8xmM+rq6lhHsVtUnjx37NgxAMDw4cMZJ7FfJpMJx44dw9WrVzF48GAkJCTQyMYOubq6wt/fHxzHQa1Ww2AwsI7ksMRiMTw9PVFbWwuz2cw6jl2i8uQxrVaL1NRUDB06lCZb3ITBYMCRI0egVqsxfPhwREZGso5EbkEsFiMgIAAuLi6oqqqCXq9nHclh+fj4wGKxoLa2lnUUu0TlyWM06rw1vV6PX3/9FRqNBqNHj0ZAQADrSKQdhEKhdRGF2tpaKtDb1HpB8/r6ehp9toHKk6do1Hlrer0eBw8eRFNTE8aMGcPrS4c5IoFAAB8fH0gkEirQDvD29gYAmnnbBipPnkpLSwPHcTTqbIPBYMChQ4fQ0tKCu+66i04Wd1ACgQDe3t7WAqVjoLYTiUTw8PBAfX09reb0B1SePGQwGHD06FEkJSXRqPMPjEYjDh8+DK1WizFjxlBxOrjfF2hNTQ0V6G3w8vKC2WxGQ0MD6yh2hcqTh9LT06HX65GcnMw6il0xm8349ddfrSNOT09P1pFIJ2gtULFYjLq6OhiNRtaRHIpYLIZCoUBdXR2NPn+HypNnOI5DSkoK+vbtS+XwOxzHITU1FVVVVRg2bBhdFNjJtB4DdXFxQX19PSwWC+tIDsXb2xtGoxFNTU2so9gNKk+euXLlCqqrq+lY5x+cP38ehYWFuOOOO+Dn58c6DukCrWviCoVCOoZnI6lUCrlcTqet/A6VJ88cO3YMISEhCAkJYR3FbhQWFiIjIwMJCQkIDQ1lHYd0odYJMGazGY2NjazjOBQvLy8YjUa0tLSwjmIXqDx5pKKiAnl5ebjjjjtohZz/U19fj+PHjyM8PBx9+vRhHYd0AxcXFygUCuh0Omi1WtZxHIabmxvEYjE0Gg3rKHaBypNH0tPToVKp0LdvX9ZR7ILBYMDhw4ehUCgwbNgw1nFIN5LJZJDL5WhqaqIZuDbw8PBAU1MTLZoAKk/eMBgMOHHiBPr16weRSMQ6jl1IS0uDTqfDqFGj4OJCFxjiG3d3d0gkEjQ2NtIEonZqvXgEjT6pPHnj/PnzMBgMGDx4MOsoduHSpUvWXdh0NRn+8vDwgEAgoFmk7SQSieDu7k7lCSpP3jh16hSio6PpFAwAdXV1OH36NHr37k0ThHhOIBBAqVTCZDJBp9OxjuMQlEolTRwClScvVFdXIz8/H0OGDGEdhTmLxYKjR4/Cy8uLRuEEwLUJRDKZDC0tLXQsrx1cXV0hkUh4v+IQlScPpKenQyaT0WxSABcvXkRNTQ2SkpLo2C+xcnV1hUAgQHNzM+soDkGpVEKr1fL6WDGVp5OzWCxIT09HQkICxGIx6zhMNTY24syZM+jTpw9UKhXrOMSOCAQCuLm50e7bdmqdJ8DnDxtUnk7u6tWrAEC7KHFtgQhXV1cMGjSIdRRih8RiMaRSKVpaWng9omoPkUgEV1dXXk+0ovJ0chkZGRAKhQgODmYdhanc3FxUVVXhjjvuoNNSyE3J5XIIhULeT4ZpDzc3N14fJ6bydGIWiwUXLlxAfHw8r1cUMhqNSEtLQ48ePdCjRw/WcYgdEwgEkMvlMJlMMJlMrOPYNTc3N14fJ6bydGJXr15Fc3Mz4uPjWUdhqvUc16SkJNZRiAMQi8VwcXGBXq9nHcWu8X3XLZWnEzt37hy8vLx4PdpqaWnB2bNn0bdvX7i7u7OOQxyETCaD2Wyma3/+CXd3d+h0Ol6O0qk8nVTrLtt+/frxepdtZmYmRCIR70ffxDYikYhGn+0gl8shEol4ueuWytNJFRYWorGxkdelodVqcfHiRfTr1w9SqZR1HOJgpFIpLBYLjT5vQSgUQiaT8fL0HipPJ3Xp0iUEBgbyevm5jIwMiEQi9OvXj3UU4oBEIhHEYjGNPv+Eq6srdDod707vofJ0UllZWQgKCuLtLlutVotLly4hPj4eEomEdRzioKRSKTiO4+UxvfaSy+XgOI53o08qTyfU2NiI8vJyxMbGso7CzLlz5yAWi+napaRDhEIhJBIJlectuLi4QCwW8+7C4lSeTig7OxsAeFueRqMRWVlZiI2NpVEn6TAXFxdYLBbeLgbQHq6urrxbWILK0wlduXIFPXr04O2pGTk5ORAKhTTqJJ1CJBJBKBTS6PMW5HI5zGYzDAYD6yjdhsrTyXAch+zsbPTs2ZN1FGaysrKgUql4++GBdD4XFxeYzWZwHMc6il2SyWQQCoW8mlxF5elkKioq0NjYyNtdtjU1NaisrETv3r1ZRyFOpPXydTT6vDmpVMqrSUNUnk4mLy8P7u7uiIiIYB2FiUuXLsHV1RXh4eGsoxAnIhAI4OLiQuV5CzKZjEaexHFlZ2fDz8+Pl1cOMZvN1l3WQiG9tUnncnFxAcdxvDufsb34tqgEbWGcCMdxKCgo4O2oq7CwEAaDgXbZki4hFAohFoupPG+idRUvvow+qTydSH19PRobG3lbntnZ2fD09ISXlxfrKMRJCYVCKs+bEAgEkEgkVJ7E8RQUFAAAwsLC2AZhwGQyoby8HNHR0ayjECfWejiAZt22TSqVUnkSx1NQUABfX19enqJRWlqKxsZG3k6UIt2jdblLGn22rfVSbnxYUIJ/s0qcWEFBAS9HnQBQXFwMd3d3+Pj4sI5iNwwGAyorK1FVVYWmpiZoNBoYjUaYzWbI5XLI5XIoFAr4+vrC39+frjzTTq27bltPXyH/I5FIIBAIYDAY4OrqyjpOl6LydBJmsxktLS28Pd5ZWFjI6yvI6PV6ZGVl4ezZs6iursbx48ehVqthMBggEAjQv39/XLx40brQeXh4OPR6vXVXd01NDXr27AmlUomEhATExcUhIiKCZi23oXW1IY7jeHvhhZtpXY3JaDRSeRLHUFVVBbVajYCAANZRul1zczNqamowZMgQ1lG6lVqtxqFDh3D27FmUlZUhMzMTcrkcY8eOxYgRIxAREYEePXrA398f3t7ecHNzs57CxHEcmpubUV9fj5qaGqjVapSWliIjIwN79+7Fv/71L/Tp0weRkZEYM2YMoqKiqCj+T+sHChp9tk0sFvPidBUqTydRUVEBALwsz6KiIgBASEgI4yRdT6vV4sCBA/juu++g1WqRlZWFSZMmYeLEiXjxxRfRs2fPdm3QBQIB3N3d4e7ujuDg4OseMxqNuHjxItLT03Hw4EGkpaXBw8MDDzzwAO644w4qDFwbYdGHibZJJBJeLBJP5ekkysvLoVAoeDlZqKysDCqVyql3E6nVamzevBlZWVlIS0tDYmIiZsyYgTFjxkCpVHbqzxKLxUhISEBCQgLmzZuH9PR0HDt2DO+88w527tyJadOmYcSIEbwuD/oAcXNisRiNjY2wWCxOvdufytNJlJeX83LUCVw73hkZGck6Rpe4evUqPvnkE+zZsweurq547LHH8Oqrr3bbxDChUIghQ4ZgyJAhmDJlCn788Ue88847SE1NxfTp03k7QY3cnFgsBnBtD4YzT0Kj8nQSFRUVvLySilarhdlsRlBQEOsonaqqqgpvvfWW9dqszz//PKZPn850z0JERAQWLVqE0aNHY/v27XjppZcwffp0TJgwgUZixMrFxcU6qcqZy9N5x9Q8YjKZUFVVxcuRZ3V1NRobG6FSqVhH6RR6vR6fffYZ7rzzTuzbtw9TpkzBzp078dhjj9nNLvk+ffpgzZo1+Mtf/oIdO3Zgw4YNaGhoYB2rW+3fvx/JyckICwtDcnIy9u/fzzqS3WhdRN/Zz/Wk8nQClZWVsFgsCAwMZB2l29XW1kIoFMLDw4N1lA47ceIExo0bh6+//hqzZs3C0aNHMWfOHEgkEtbRbuDi4oIpU6ZgxYoV0Ov1WLNmDUpLS1nH6hbz58/HuHHjcOLECRQVFVn/3h577DHW0eyGSCRy+ivQUHk6gaqqKiiVSvj5+bGO0u2qq6vh7e3t0BMTmpubsXz5cjz00EPo378/Nm7ciBUrVjjEB4JevXrhqaeegp+fH9avX4/c3FzWkbrU/v37sXnz5jYf27RpEw4ePNjNiewTjTz/j0ajsflGuk9NTQ20Wi3c3NxYR+l2tbW1Dr2qUGZmJqZNm4a9e/di7dq1ePfddx1ufV4vLy88++yzCAwMxLZt23D16lXWkbrMqlWrbvn4ihUruimJfaOR5/9pvVJFe2/e3t5O/Q/I3tTW1sLb25uXpw7U1NQ4ZHlyHIevv/4a9913H0wmE77//nvMnTvXYUfQrq6uWLJkCVQqFd59912Ul5ezjtQlysrKOvQ4X/Dh2qftnm377bffwtvb+0+/j+M4TJw4sUOhiG3q6ura9XfjbLRaLVpaWhzud29pacGSJUvw3Xff4fnnn8ff//536/R+RyaVSrFgwQJ88skneP/997F8+XIoFArWsTpVUFCQdVGOmz1O/ncerMlksstj9p2hXeUZFhaGO++8s92f8CMjI51iY+AoamtreXm+XX19PSQSiUNdv7OyshKzZ8+GQCDAxo0bMXnyZNaROpWrqyvmzJmDN954Azt27MD8+fOd6jSWV155BePGjbvp46+99lo3prFfrctAOnN5tmsfUX5+vk27xi5cuMCLpdLsBV9Hnk1NTRCJRJ2+wk5Xyc7Oxvjx41FWVoa33nrL6Yqzlbe3NxYsWIDCwkKnO4Xj7rvvxoIFC9p8bMGCBRgzZkw3J7JPAoEAIpHIqa976pgHWIiVwWCA0WiEp6cn6yjdTqvVoqmpySFOxD516hSmTJmC3r174+eff0bfvn1ZR+pSPXv2xNChQ3HixAmnO4Xls88+w4EDBzB06FDIZDL4+PjgwIED+Oyzz1hHsysikcipZ9y2+5jnkiVL2rzfw8MDsbGxePDBBx1iI+ZsGhsbodPpnO7YUnvodDqHeM/99ttvWLRoESIjI/HJJ584zEi5oyZMmIDMzEx8/fXXWLp0qcNOhmrLmDFjMGbMGCxYsAB5eXk04mxD63VPnVW7381nz55t87Z79248/vjj6NOnzy0PpJOuodVqAYCXp6no9XrIZDLWMW7p2LFjePjhhzF48GDs2rXLrovTYrFg+/btnfZ8IpEIM2bMQHNzM06fPt1pz2tPAgICnHZmcUdRef6fw4cPt3k7e/YsSktL0bt3b7zwwgtdmbXdPvzwQ4SHh0MmkyEpKQknT55kHanLNDc3AwDkcjnjJN1Pr9fb9cjz1KlTePTRRzF06FB8+OGHdn/Vl3feeQczZ87E22+/3WnPGRkZiejoaPz444/Q6/Wd9rz2Ijw8/IZLupFrqDzbQalUYuXKlTh+/HhnPF2H7Ny5E0uWLMHq1atx5swZ9O/fH+PHj0dlZSXraF2CRp72OfK8ePEiHnroIYwePRpff/213eb8vU2bNgEAPv/880593nvuuQdisRhpaWmd+rz2QKFQQCAQOP2CALdDJBJRebaHr68vamtrO+vpbtuGDRuwcOFCzJs3D3Fxcfjkk08gl8s7fYNgL7RaLQQCgUNsnDubvR7zLC4uxuzZsxEaGop3333Xrkec8+fPx4QJEzBhwgRcvnwZAHDp0iXrffPnz+/wz/D19UV0dDSOHDnidBNIzGYzUlNTnXpW6e0SCAROXZ6ddkmyEydOICoqqrOe7rYYDAakp6dj+fLl1vuEQiHGjh2L1NTUNv+MXq+/bneSoy0tqNVqIZfLebm6kEAgsLvd1U1NTXj44YehUqnwxRdf2PVErqamJmzZsuWGDT/Hcdi3bx+Aa6/xe++91+EruowaNQoFBQU4d+4cBgwY0KHnIo5BJBJBKBSC4zin3D61uzzPnTvX5v0NDQ1IT0/H66+/jtWrV3dasNtRXV0Ns9kMf3//6+739/e3fqr+o3Xr1uHll1/ujnhdorm52a5HNl3J3kYxFosFL730EgoKCnDo0KEb3of2xt3dHSdPnsTYsWPbvKSYh4cHDh061CmXQgsICICvry9OnDjhlOVJI8+b4315JiQkQCAQtPkm8fX1xZIlS/DEE090arjusHz58utOw9FoNA61wINOp7O70Vd3MRgM0Ol0rGNYvf3229i6dSt27dqF3r17s47TLoMHD0ZFRUWbH8AqKio69XDAkCFD8N1336Gqqspprr/qjKXQWVpfG2f9YNHu8szPz2/zfqVSaTfLo/n6+kIkEkGtVl93v1qtvumFoqVSqV0eN2uvlpYW3i6FKBaLYTQaWccAABw5cgSvvPIKli1bhrvvvpt1HJt8+eWXbd7/1Vdf3XQ1ndsRFxeH7777DufPn8ddd93Vac9L7JOzl2e7JwyFhYW1eWstTovFgh9++KHLgraHRCLBoEGDrrumnsViwcGDB5GcnMwwWdcxm83WdST5xl7Ks6KiAsuWLcPIkSPx4osvso5jsy+++AIAEBISgpSUFOupF1u3bu3UnyMWi9G7d29cuXKlU5+X2CdnH5V3eKubm5uLzz//HFu2bEFVVRXzjdmSJUswZ84cDB48GImJiXj33XfR3NyMefPmMc3VVcxms1MtvG0LsViMlpYWphk4jsNf//pX6HQ6fP755w75d/HUU09h6NCheOONNyAUClFYWIgXXngBgwYN6vSfFRcXh19++QUNDQ0OcbHvPyMSiZCUlOT0RXE7nH3keVvl2dLSgl27duGzzz7D8ePHMWLECKxatQoPPPBAZ+ez2bRp01BVVYVVq1ahoqICCQkJ2Ldvn91P3rhdfC9Pg8HANMPmzZtRUlKCt956C35+fkyz3K5p06Zh2rRp1q+FQiHefPPNLvlZ0dHR2LVrF/Lz85GQkNAlP6M7tbS0QC6X8/bQSXs4a3nadJ7nqVOn8Ne//hUBAQF49913MXnyZAgEAnz00Uf429/+ZjcFtWjRIhQWFkKv1yMtLQ1JSUmsI3UZvpcny5PTKyoqsHz5cgwcOPCWl6ki/yOXy+Hv73/TORSOprCwEAUFBaxj2CVnH3m2uzzj4+MxdepU+Pj4ICUlBWfOnMHSpUtpdwVjFouFt+Xp4uLC9DDB4sWLIRaL8cYbbzDL4Iiio6OdZsWvyspKuxk02BuBQAChUOi0HdHu8rxy5QruvPNOjB49GnFxcV2ZidhALpfzcnUh4NqShKw+1f7www/47rvvsGHDBpuudUuunfPZ3NzMfJd7Z6ioqLjpTH6+c9YRZ6t2l+fVq1fRs2dPPPHEEwgODsZzzz2Hs2fPOu2nCkfR3NxsXRyeb9zd3VFbW2td37er7d+/H8nJyQgNDcXcuXMxaNAgTJ06tVt+tjPx8/ODRqNBVVUV6ygdplaraeTJU+0uzx49euCll15Cbm4utm3bhoqKCtxxxx0wmUzYsmULsrOzuzInuQl7OV2DBW9vbwBATU1Nl/+s+fPnY9y4cThx4gSKi4tRU1OD1NRULFy4sMt/trPx9fWFQqGwi7WwO+pW55AT53ZbC8Pfdddd+PLLL1FeXo4PPvgAhw4dQq9evRAfH9/Z+cifYD1phqXW8uzqjfD+/fuxefPmNh/btGnTdecVkz8nkUhgsVhQX1/POkqHGI1G1NbW0sjzJlp32zrr3skOXVXFw8MDTz75JE6fPo0zZ85g1KhRnRSLtBefR55isbhbRjCrVq265eMrVqzo0p/vjDw9PdtcT9eRlJWVgeM4hIWFsY5CGOi0S5IlJCTgvffe66ynI+3EesYpa97e3l1enmVlZR16nNxIpVLZ3cL+tsrLy0NSUhLzq0nZO16PPAcOHIi6urp2P+nw4cNRWlp626FI+/F55Al0T3kGBQV16HFyI4FAgKamJtYxOiQjIwOXL1+2LmdIrsdxnFOfqtKuFYYyMjKQmZlpPcbUnu///TUySdfhe3n6+PggKyurS3/GK6+8cstFEF577bUu/fnOyB5Wh+qozMxMxMfHO205dJSzH/Ns9/J8Y8aMafd5O876YtkjV1dXSCQS1jGYUalUkMlkXbpW6t1334358+fj888/v+GxBQsWYMyYMV3yc52ZRCJx+A99586dw6RJk1jHsFtUnrj55chuhXZldA8XF5cbLsHGJ0FBQaitrUVhYWGXzvb+9NNPMWPGDKxcuRJlZWUICgrCa6+9RsV5myQSiUNfCrC2thZFRUXo378/6yh2i8oToNlkdkyhUECn08FkMvHy0mRubm5QqVQoKCjosvJs3QiMHTsWY8eO7ZKfwTcWi8Whd9ueP38eAKg8b4HjOKctTqATZ9sSNhQKBQCgsbGRcRJ2IiIiunRxbmdfZowFR/+wd+XKFQwbNgyRkZGso9gtKk9i11rL09FnLnZEWFgYampquuwDhMViceqNAAuOXp4HDx6Eq6srhELahN6Ms/+7ob95B0cjTyA8PBwAumT0abFYADjvcRtWzGYz3NzcWMe4LXq9HrW1tZgwYQLrKHat9VQVZ+W8vxlPuLu7A+B3ebq7u1uPe3Y2Z9/1xIpOp3PYqwEdP34c586dQ3JyMusods+ZL5doc3nOmTMHR48e7Yos5DZIJBIEBwfzerctcG302dnlyXGc0396ZqWxsRFyuZx1jNvyyy+/ICQkBD179mQdxa5ZLBan/rdj82/W0NCAsWPHIiYmBq+//jqtJMSYQCCAyWTi9ekqABAZGQmTydSpV1gxm80wm8008uwCjY2N1kMOjoTjOPz8888YP348vS/+BB3z/IPdu3ejtLQUTzzxBHbu3Inw8HBMmDAB3377rcOf9OyoVCqVU1wbsSOio6PR0NCACxcudNpzOvs/flZ0Oh2kUmmXLWrRlbKyslBWVnbLFafI/+YK0MjzD1QqFZYsWYLMzEykpaUhOjoas2fPRlBQEBYvXoycnJzOzkluQaVSobq6mnUMpiQSCeLi4nD27NlOO7XEYrE49TEbVlovYO7p6ck6is0OHToEd3d3DBs2jHUUu9b6b5DK8ybKy8uxf/9+7N+/HyKRCBMnTsT58+cRFxeHd955p7Mykj/h6+uLqqoq3p+PmJCQgKqqKpSXl3f4ufjwyZmVuro6iMVihyzP7777DlOmTIFYLGYdxa7x4d+Pzb+Z0WjEv//9b9x3330ICwvDrl278Oyzz6KsrAxbt27FgQMH8M033+CVV17pirykDSqVCkajERqNhnUUpqKjo+Hm5oaMjIwOP1frLlvabdv5qquroVAoHO48z4sXLyI7Oxvjx49nHcXu8eHfj83v3sDAQFgsFsyYMQMnT55EQkLCDd8zevRoh/xU6ahUKhUAoKqqyiGPI3UWoVCI+Ph4nDt3Dvfcc0+HPvXSRKGuU1lZCT8/P9YxbLZ9+3bExMRg1KhRrKPYPYvF4nAfjmxl89blnXfeQVlZGT788MM2ixO4dpX421lMntweX19fAOD9pCHg2q7bxsZGXL16tUPPYzabnXqXEytmsxm1tbUIDAxkHcUmzc3N+PbbbzFhwgReX8WovZz9NBXgNspz9uzZDntys7OSSqWIjIzk/aQhAOjRowe8vb2RmZl528/Bh+M1rFRWVsJoNDpcee7evRtNTU2YNWsW6ygOgcqTOAyJRNKli6M7CoFAgOTkZFy9evW2F46wWCy8+MfPQllZGSQSiXVviSPgOA5ffPEFxowZQ5dabIfWxUWcfaY6bR2cRGhoKIqLi1nHsAsJCQnQaDT47bffbuvP0/mdXaekpATBwcEO9cEkPT0dFy5cwJw5c1hHcQhmsxmA8++5ce7fjkeCg4NRVVWFlpYW1lGYk8vlSE5ORmpq6m29HlSeXcNgMKC8vByhoaGso9jks88+w1133YWRI0eyjuIQ+HLYw7l/Ox5p3SCVlJQwTmIf7rzzTpjNZqSkpNj8Z2mmbdcoLi6Gi4sLwsLCWEdpt/z8fPz0008YP3680++G7Cx8WVyEytNJBAYGQiQSoaioiHUUu+Du7o7ExEQcO3YMBoPBpj9LV1LpGlevXoWnp6dDrWm7ceNGjBgxAlOnTmUdxWFQeRKH4uLigqCgICrP3xk5ciR0Oh3S0tJs+nN0JZXOZzKZUFJSgsjISNZR2i07Oxvbt2/HuHHjIJVKWcdxGFSexOHExsbSjNvf8fT0xMCBA3HkyJF2jz5bZwrSyLNzFRQUwGg0Ijo6mnWUdnvrrbcQHByMGTNmsI7iMPgyWQig8nQqoaGhKCwspElDvzN69GgIBAKkpqa26/upPLtGdnY2AgICoFQqWUdpl7Nnz+Lnn3/Gc889R+vY2qB1shCNPIlDiY2NBcdxyM3NZR3Fbvj6+mLAgAH4+eef2732L98X2O9sTU1NqKurc5iLR3Mch3feeQe9e/fG/fffzzqOQzGbzbwoToDK06n4+/tDoVAgOzubdRS7ctddd0EsFuM///nPn34vx3HWT8+kc1y6dAlmsxlRUVGso7TLvn37kJ6ejpUrV/Ji92Nn4tPiIvz4LXlCIBAgNjaWyvMPXF1dMWnSJJw9e5Zem25mNpuRl5eH2NhYh1goXKvV4tVXX8XQoUNxxx13sI7jUFo/eNLIkzik2NhYXL16FSaTiXUUuzJo0CBERkbi3//+N7023Sg7OxstLS2Ii4tjHaVd3n//fQQFBWHVqlWsozic1sVFqDyJQ4qNjYXBYEBhYSHrKHZFIBDgoYceQm1tLQ4fPnzL76Ndt53DYrHg/PnzCA8Pd4iJQmfPnsWnn36KcePGOdRCDvai9UpEfJlsR+XpZMLCwiCXy5GTk8M6it0JCAjAqFGjcODAgZtevq21PGnSUMfl5+ejqakJ/fv3Zx3lT+l0Oixbtgzx8fFYsGAB6zgOiU+ThQAqT6cjEokQFRXVoUtyObO7774bgYGB2L59u/WctN8TCAQQCAQ08uwgi8WCc+fOISIiAt7e3qzj/Kl//vOfKC4uxptvvsmrAugsfLmSyu9ReTqh+Ph4XL58GTqdjnUUuyORSHD//fejuroav/zyS5vfIxQKqTw7KC8vDy0tLYiPj2cd5U+dPn0aKSkpePbZZx1qEQd7wqfFEVrx5zflkf79+8NkMiErK4t1FLsUGRmJ4cOH4+eff8bly5dveJxGnh1jMBhw9uxZhISEwMfHh3WcW2poaMDixYshl8uxcOFC1nEcFt+OdwJUnk7J398fAQEBtOv2Fu6++2707t0bX3zxBerr6697TCgU0ozcDjh37hxMJhMGDRrEOsotWSwWvPLKK2hpacGGDRt4tcuxs/HpFJVWVJ5Oqn///sjMzKSJLzchEAjwyCOPQCwWY/Pmzdcd/xQKhTAajQzTOa6GhgZcunQJ/fr1g1wuZx3nlj766CMcOnQI7777LgIDA1nHcVgWi4V3xzsBKk+n1b9/f9TU1KC0tJR1FLvl5uaGefPmobi4+LrVh8RiMSwWS5sTisitnTp1Cu7u7nZ/Xucvv/yC999/HwsXLsTw4cNZx3ForaNOPh3vBKg8nVavXr0QFBREu27/RHh4OO6//36cP38ep06dAgDrQuA0+rRNfn4+amtrMWTIELsehWRnZ2PZsmUYP348nnjiCdZxHF7r8U6+4d9vzBNisRjBwcE4fvw46yh2b+TIkdbVh3JyciAUCiEUCm2+iDafNTc34/Tp0wgJCUFwcDDrODdVXV2NdevWISwsDOvXr+fVBJeuwMdTVFpReTqx5ORkFBYWoqysjHUUuyYQCDBjxgyEh4fjk08+QVFREcRiMfR6PetoDoHjOJw4cQJisRiDBw9mHeemmpqa8Pjjj+Pq1av45JNP4OrqyjqSwzObzRAIBDTyJM6lf//+kMlkOHHiBOsodk8kEmHu3LkICAjABx98gLq6OhiNRjru2Q5XrlyBWq1GcnKy3V770mAwYPHixSgpKcHGjRtpglAn4esuW4DK06mJxWIMGTIEqampNOu2HWQyGZ588kl4eHjg008/RW1tLS008Sfq6+tx6dIl9OrVC/7+/qzjtMlgMODZZ59FdXU1PvjgA4e5rqi94/MuW4DK0+klJyejrKwMxcXFrKM4BDc3Nzz99NOQSCTYunUr1Go160h2y2Aw4NixY5DL5Xa7fm1rcaampuL5559HYmIi60hOg8+7bAEqT6fXt29fuLu7IzU1lXUUh6FUKvHMM89ALpfjo48+Qm1tLetIdqf1OKdAIMAdd9xhl6MPvV6PxYsXIzU1FR988AGGDRvGOpJT4fOoE6DydHoikQiJiYk4c+YM7bq1gY+PD5588kno9Xr885//RGVlJetIdiUjIwNqtRqDBw+Gu7s76zg30Gq1+Pvf/46qqiq8//77dGHrTsbXhRF+j8qTB0aMGIGioiJa69ZG/v7++Pvf/w6dTod169YhLy+PdSS7kJeXh5ycHAwcONAuj3PW1dXhscceQ0ZGBpYuXUqLIHSB1gtf8/lUHypPHoiJiUGPHj1w4MAB1lEcTlhYGObNmwdfX19s2LABp0+fZh2JqaKiIpw9exa9evVCVFQU6zg3KCoqwooVK1BaWorNmzcjKSmJdSSnZLFYeHussxW/f3ueEAgEGDNmDE6dOgWNRsM6jkMRi8Xw8fHBrFmzMGDAAHz66af4+eefebkLvLy8HKdOnUJ4eDj69evHOs4NUlNTMXPmTJSWluLLL79E7969WUdySq1XHKLyJLwwYsQICIVCHDlyhHUUh+Pp6QmBQIC//OUvmDhxIr7//nts376dV8v3qdVqpKamIigoCIMGDbKr3XUcx+Hrr7/Gk08+ifj4eGzbtg0hISGsYzktPl5+rC1Unjzh7u6OpKQkHDp0iJejpo4Qi8VQKBTQaDS47777MH/+fPz222948803UV1dzTpel1Or1Thz5gwCAgKQlJRkVxtNrVaLVatW4auvvsKsWbPwwQcfQKFQsI7ltFq3HXwfdQJUnrwyduxYqNVqXLhwgXUUh+Pp6QkAqK2tRWJiIl544QWIRCKsXr0aaWlpbMN1oaKiIpw4cQJeXl5ISkqyq41mTk4OZs2ahYMHD+Lpp5/Gc889Z1f5nBHHcbw+t/P36BXgkdjYWERGRiIlJYV1FIcjFArh5eUFjUaD5uZmhIWF4ZlnnkFCQgI2btyIjRs3QqvVso7ZqXJycnDmzBmEhoYiKSnJbk5LsFgs+Prrr7Fs2TKIxWJ8/fXXuOeee1jH4gWaKPQ/9CrwiEAgwOjRo3H48GFUVFSwjuNwFAoF3NzcoFarYTQaIZfLsXDhQjz++OM4d+4cVq9ejcuXL7OO2WEcx+HcuXO4ePEievXqhQEDBtjNrtri4mI8/vjjePvtt3HXXXdh27ZtCA8PZx2LF2ii0PXoVeCZO++8E0qlEj/++CPrKA7Jz88PIpEI5eXl1uM/SUlJeOWVV6BSqbB161Z88cUXaGlpYZz09hgMBpw4cQLFxcVISEhAr169WEcCcG2Syrfffovp06ejsrISGzduxNNPPw2pVMo6Gm/QqPN69ErwjEQiwT333IPDhw+joaGBdRyHIxQKERAQAKPRiLKyMmuBent747nnnsPYsWORkpKClStXIiUlxaEmZ9XX1+P48eNoaGhAUlKS3Yzozp07h0cffRQffPABHnroIezYsQODBg1iHYtXWt/H9rIHwh4IOEf6190NNBoNPDw80NDQAKVSyTpOl2hqasKTTz6J++67Dw8//DDrOA5Jq9WitLQUbm5uCAwMvG6jUldXhz179uDw4cOIiIjAzJkzERsbyzDtrXEch9zcXGRnZ8PLywsDBgywi2tdVlVVYcuWLfjmm2/Qu3dv/OMf/0CfPn1Yx+Kl1kvz2ctx765iy/afyvMP+FCeALB161b8+uuv+OijjyCTyVjHcUjNzc0oKyuDu7s7AgICbvhUfvnyZWzfvh0FBQUYMmQIpk2bBpVKxSht2zQaDc6fP4/m5maEhoaiZ8+ezEcXjY2N2Lp1K3bu3ImwsDA8+OCDmDJlCu0yZMhkMkEkEjF/b3Q1Ks8O4Et5VlVV4ZlnnsGjjz6KCRMmsI7jsJqamlBaWgq5XI6goKAbPplzHIeUlBTs2rULrq6uiImJwf333w9fX19Gia8xm83Izc3F1atX4ebmhvj4eOvpOKw0NTXhv//9LzZt2gSTyYSZM2di1qxZcHNzY5qL7/g0UYjKswP4Up4A8Omnn6KgoABr1qyBWCxmHcdhNTc3o7S0FEKhEMHBwW2O5A0GAw4cOIAffvgBWq0Wo0aNwl133YXQ0NBuz1tVVYWLFy9Cp9MhOjoakZGRTDeMdXV12LFjB/7973/DbDZjypQpmD17Nry9vZllIte0XvCaL4vA87Y8w8PDUVhYeN1969atwwsvvNDu5+BTeZaWlmLx4sWYO3cuJk6cyDqOQzMYDCgpKYFer4evry98fX3b3Njo9XocOXIE//3vf1FXV4e4uDjcc889GDBgQJcXWG1tLfLy8lBTUwOVSoVevXoxHdVduXIF3333HbKyslBaWooHH3wQ06dPZz4qJ//Dp1EnwPPyXLBgARYuXGi9r/XcvPbiU3kCwEcffYQzZ87ggw8+oGOfHcRxHNRqNWpqaiCRSBAUFHTT957ZbMapU6ewb98+5OTkICQkBMOGDcPw4cM7fcRVXV2NgoIC1NbWQqFQIDo6mtmxV61Wi19//dVamn5+fpg+fTomTJjAi39vjoRvo07Atu2/Szdl6jYKhQIBAQGsYziMqVOn4ujRo9i7dy8efPBB1nEcmkAgQEBAADw9PVFWVob8/HzrZKI/fjARiUQYOnQohg4diry8PBw7dgzffvstduzYgQEDBiAxMRGDBg267QtNt55KU1paiubmZnh4eCAhIQF+fn6d8avanOXUqVP45ZdfcOzYMfTo0QM+Pj5Yv349hg0bxptRjaOh01NuzelGnjqdDkajEaGhoZg5cyYWL14MF5ebf0bQ6/XQ6/XWrzUaDUJCQngz8gSAzz//3DrzliZndJ76+npUVFTAYDDA3d0dPj4+UCqVN90YabVapKWlITMzEydOnIBAIEBcXBySkpIwePDgPx2RWiwW1NbWQq1WQ61WA7i2qENwcHC3TwZqampCWloajh8/jkuXLqGkpAQREREYN24cxo4dSx9wHQAfL3jN2922GzZswMCBA+Ht7Y2UlBQsX74c8+bNw4YNG276Z9asWYOXX375hvv5VJ719fVYtGgRJk6ciJkzZ7KO41Q4jkNDQwOqqqrQ3NwMgUAAhUIBDw8PeHh43PSDXV1dHU6fPo2TJ0/i4sWLUKlUEIlE6NevH/r27YuePXtCoVCgqakJDQ0NqK2tRX19PTiOg6urK/z9/REYGAiJRNItv6der8fFixeRmZmJrKwspKenw2w2IyYmBsOGDcOoUaMQERHBqw0xcTxOVZ4vvPAC1q9ff8vvuXTpUpvLiH3++ef461//iqamppsu40Ujz2u+/vpr7N27F++//z68vLxYx3FKOp0O9fX1aGhoQHNzMziOg1QqhaurK2QyGaRSKcRiMYRCofUGXPsgl5mZiczMTOsVcUpKSqBUKhEcHIzg4GDExMSgd+/eCA8Ph1wu7/Lfo7CwEDk5OcjJyUF2djbKy8ut/2b69++PxMREJCUl2d15rYTcilOVZ1VVFWpqam75PZGRkW1+wr548SL69u2Ly5cvo2fPnu36eXybMNSqubkZr776KsLCwvDEE0+wjuP0TCaT9QotWq0WOp0OOp3uhuX8WidtAP879qTValFZWYny8nKUlpaiuLgYcrkcDQ0NUCgUiImJse4mbr15eHjA3d0dcrkccrkcYrH4uktLcRxnzaDT6dDY2Ii6ujrU1dWhtrYWtbW1KCwsRGlpKaqqqiAWi2EymRAWFobY2Fj069cPvXr1Qnh4OI0uicNyqglDKpXqtj+9ZmRkQCgUMpkk4Wjc3NwwcuRIbNq0CePGjUNUVBTrSE7NxcUF3t7e1x3HNJvNMJlMsFgs1hvHcRCJRHBxcYGLi0uby6OZzWaUlJSgtLQUJSUlaGhowNWrV3Hp0iXU1NTAZDJBoVBY1zJ2c3NDY2Pjdc/h5eVl/ZDaOsOy9ZiXp6cnoqKi4OHhgbi4OAQHByM8PBxhYWG0MDvhLbsfebZXamoq0tLSMHr0aCgUCqSmpmLx4sWYMGECtm7d2u7n4evIE7i2EX7++echlUrx+uuv0wjCCXAcB41Gg/r6emi1Wmi1WrS0tECv11tHtRzHWctZKpVCJpNBoVDAy8sLSqXS6dczJaSVU40820sqlWLHjh1Ys2YN9Ho9IiIisHjxYixZsoR1NIchEomwYMECrFq1Cr/++itGjRrFOhLpIIFAYJ2cRAjpPE5TngMHDsSJEydYx3B4ffr0wR133IFt27YhMTGxyyefEEKII6Kzk8kN5syZg5aWFnzzzTesoxBCusj+/fuRnJyMsLAwJCcnY//+/awjORQqT3IDHx8fTJs2Denp6cjPz2cdhxDSyebPn49x48bhxIkTKCoqwokTJzBu3Dg89thjrKM5DCpP0qZ7770XIpEI77//vvVCuIQQx7d//35s3ry5zcc2bdqEgwcPdnMix0TlSdrk4uKCp59+GoWFhfjuu+9YxyGEdJJVq1bd8vEVK1Z0UxLHRuVJbioqKgoPPPAAdu7ciaKiItZxCCGdoKysrEOPk2uoPMktTZs2DYGBgbT7lhAnERQU1KHHyTVUnuSWxGIxnn76aeTl5WHPnj2s4xBCOmj16tW3fPy1117rpiSOjcqT/KnY2FhMnjwZO3bsoN23hDi4zMzMm64etmDBAowZM6abEzkmKk/SLjNmzEBcXBzefvttGAwG1nEIIbfh9OnTWLNmDV588UUcOHAAQ4cORWhoKIYOHYoDBw7gs88+Yx3RYTjN2radhc9r2/6Z/Px8PP/88xg/fjwWLlzIOg4hxAZNTU0YMmQIPDw8cPTo0W671qsjsWX7TyNP0m4RERGYN28efvjhB6SlpbGOQwixwdKlS1FWVoZt27ZRcXYCKk9ik4kTJyIpKQnvvfceqqurWcchhLTD999/j88//xzvvPMOYmJiWMdxClSexCYCgQDPPPMMZDIZ3n77bTp9hRA7V1hYiM8++wwPPvgg5s2bxzqO06DyJDZzd3fH0qVLUVtbi6+++op1HELITbS0tODhhx9Gbm4uPv74Y7pGbyei8iS3JS4uDhMmTMCuXbvw66+/so5DCPkDjuOwaNEiXL58Gd988w28vb1ZR3IqTnM9T9L9Jk+ejPz8fLz33nsICgqiYymE2JF//etf+PLLL7F582b079+fdRynQyNPctsEAgGeeuopREREYO3atairq2MdiRACIDU1FUuXLsWTTz6JmTNnso7jlKg8SYdIJBK8+OKL4DgOr7/+OoxGI+tIhPBaYWEhXnrpJdx9991Yv3496zhOi8qTdJi3tzdeeukl5OXl4eOPPwatu0EIG/X19Zg8eTIqKirw6aef0vmcXYjKk3SK2NhYPP3009i/fz9++OEH1nEI4R29Xo+pU6eisrISe/bsgUqlYh3JqdGEIdJpRo8ejYqKCmzZsgU+Pj4YNmwY60iE8ILFYsHChQtx6tQp/PTTTzR5rxvQyJN0qunTpyMxMRFvvvkmzp8/zzoOIbywatUqfPvtt9iyZQuSk5NZx+EFKk/SqQQCAZYsWYI+ffrg1VdfRUFBAetIhDi1jRs34u2338b69esxZcoU1nF4g8qTdDqxWIyXXnoJAQEBWLlyJdRqNetIhDilH374AYsXL8aiRYvw9NNPs47DK1SepEvI5XK88sorkEgk+Oc//4na2lrWkQhxKr/99huWL1+ORx99FG+88QbrOLxD5Um6jKenJ9auXYuSkhL84x//oAIlpJOkpqbioYceQnh4ON555x2IRCLWkXiHypN0qYCAALzxxhtoaWmhAiWkE5w+fRpTpkzBwIEDsXPnTshkMtaReInKk3S5oKAgvPnmm9DpdFSghHRARkYG7r//fvTt2xfffvst5HI560i8ReVJukVQUBDWr18PnU6HZcuWUYESYqNTp05h/vz5GDp0KL7//nu4u7uzjsRrVJ6k27SOQPV6PRUoITY4dOgQ7rvvPvj6+mLLli1QKpWsI/EelSfpVoGBgdcVaFVVFetIhNi1PXv24C9/+QuGDx+O3bt3U3HaCSpP0u1aC9THxwdLlixBSUkJ60iE2KVt27bh0UcfxeTJk7F9+3Y6xmlHqDwJE4GBgXjuuecgk8mwZMkSXLlyhXUkQuzKe++9hyeffBLz58/HZ599RldIsTNUnoQZlUqFDRs2ICgoCM8//zxOnz7NOhIhzHEch5dffhkvvfQSnn/+eWzYsIHO47RDVJ6EKYVCgfXr1yMhIQErV67EgQMHWEcihBmTyYQ1a9bgrbfewtq1a7Fq1SoIBALWsUgb6JJkhDmpVIrVq1dj8+bNWL9+PXJzc7Fw4UL6tE14RaPRYM6cOUhLS8OmTZvw8MMPs45EboHKk9gFkUiEBQsWQKVS4aOPPkJ+fj5WrFgBhULBOhohXa6goAAPP/wwKioqsH37dowcOZJ1JPInaLctsRsCgQCTJ0/G+vXrkZOTg0WLFtElzYjTS0lJwejRo2E0GnHw4EEqTgdB5UnsTkJCAj788ENIpVI888wzSElJYR2JkE5nsVjw3nvvYerUqRg9ejQOHjyImJgY1rFIO1F5ErsUGBiIf/7znxg0aBBWr16NL7/8EhzHsY5FSKeoq6vDzJkzsXr1ajz++OPYuHEjvL29WcciNqBjnsRuubq6YtWqVfjqq6+wdetWFBUV4dlnn6UTxYlDO336NObNm4fm5mZ88803uPvuu1lHIreBRp7ErgkEAjzyyCNYs2YNioqK8Le//Q3Z2dmsYxFiM47j8Mknn2DixIkICAjA0aNHqTgdGJUncQh33HEHVq5cCTc3Nzz99NP497//TbtxicNoaGjAnDlzsHz5cjz++OP48ccfERwczDoW6QABR1ug62g0Gnh4eKChoYEWYLZDJpMJn332GXbt2oURI0bgmWeeoWNFxK5lZmZi7ty5qK2txUcffYR7772XdSRyE7Zs/6k8/4DK0zGkpaVh27ZtKCoqwtNPP42xY8fSSizErphMJnzwwQf4+eefodPpsHnzZoSHh7OORW7Blu0/7bYlDikpKQmvvfYaEhMT8frrr+PFF1+ky5sRu5GXl4d7770Xa9euxdChQ7Fv3z4qTidD5UkclqenJ1asWIHXXnsNOTk5mDt3Ln788Uc6FkqYMRqN2LhxI0aOHImamhr8+OOPWL16NaRSKetopJPRbts/oN22jqmxsREff/wxfvrpJwwaNAjPPfccAgICWMciPHLixAksW7YMV65cwfPPP48nn3ySTqtyMLTblvCOQqHAsmXL8Oabb6K4uBjz5s3D999/T6NQ0uWqqqqwaNEiTJo0CXK5HPv378dzzz1HxenkaOT5BzTydHxarRYbN27Enj17MHLkSDzyyCOIjo5mHYs4GbPZjK1bt2Lt2rUQiURYtWoVZs6cCaGQxiSOimbbdgCVp/PIzMzEu+++i4KCAtx///1YsGAB/Z2STnHmzBksW7YMmZmZeOSRR7By5Uo6ZcoJ0G5bQgD0798fn376KZ544gns378fs2bNwu7du2E0GllHIw6qtrYWS5cuxT333AOLxYKffvoJ77zzDhUnD9HI8w9o5Omc6urq8NVXX2HXrl1QqVSYO3cuJkyYQBfcJu1iMBiwdetW7N27F5mZmXjxxRcxb948ev84Gdpt2wFUns6tsLAQn332GY4cOYLg4GAsWLAAd911Fx2nIm2yWCzYvXs31q1bh5KSEsyfPx9///vf4efnxzoa6QJUnh1A5ckPOTk5+PTTT5GamorIyEgsXLgQd9xxB61SRABcO1/zu+++wwcffAB3d3f4+fnhpZdeQmxsLOtopAtReXYAlSe/XLhwAZ9++inOnDmD3r1747HHHsOQIUOoRHmqpaUFX3/9NT766COUlZVh/PjxeOaZZzBw4EDW0Ug3oPLsACpPfkpPT8fGjRuRlZWF+Ph4zJ8/HwMHDqQS5QmNRoPNmzfj008/RX19PaZMmYJFixahV69erKORbkTl2QFUnvzFcRxSU1Oxe/duHD9+HL169cKsWbMwcuRImhjipCorK7Fx40Zs3boVBoMBM2bMwJNPPonQ0FDW0QgDVJ4dQOVJOI5DWloatm/fjtOnT6Nfv35ITEzEfffdRxNFnERhYSE+/vhjbN++HRKJBHPnzsXChQvp75fnqDw7gMqT/F52djZ27dqFAwcOwGAwIDk5GZMnT8awYcNoNOpgLBYLfvvtN2zduhWVlZXIz8/H448/jnnz5tG/dQKAyrNDqDxJW5qbm7F//37s2bMHly9fhq+vLyZNmoRJkyYhMDCQdTxyC1euXMHu3bvxyy+/IDc3FzExMViwYAGmTJkCV1dX1vGIHaHy7AAqT/JnsrOzsWfPHuzbtw8tLS1ITEzE/fffjxEjRkAsFrOORwCUlpZiz5492L17Ny5dugSlUon77rsP06dPR0JCAk0EI22i8uwAKk/SXi0tLTh48CD27NmDCxcuwMvLCw8++CCGDx+Onj170ga6m9XX1+OHH37A7t27kZaWBqlUinHjxmHKlCkYNWoUJBIJ64jEzlF5dgCVJ7kdV69exX/+8x8cP34cRUVF6NGjB0aOHIlhw4ahf//+tOHuIi0tLThw4AC+//57HD58GBaLBSNGjMCUKVNwzz33wN3dnXVE4kCoPDuAypN0hNlsRnp6OlJTU7Fv3z5UV1dDJpNhyJAhGDp0KJKTkxESEsI6pkOrrq7GsWPHcPjwYfzyyy9oamrCgAED8MADD2DSpEnw9fVlHZE4KCrPDqDyJJ2F4zjk5uYiNTUVqampyMjIgMlkQnBwMJKTk5GcnIxBgwbRRZP/RHl5OU6ePGm95ebmQqlUIiQkBJMnT8a4ceMQFhbGOiZxAk5ZnmvXrsWPP/6IjIwMSCQS1NfX3/A9RUVFeOKJJ3D48GG4u7tjzpw5WLduHVxcXNr9c6g8SVfRarVIT09HSkoKUlJSUFZWBrFYjISEBCQnJ2PIkCGIjY3l9SL1HMehsLAQaWlpOHnyJE6dOoXi4mIAQHR0NBITE5GYmIhhw4ZBpVIxTkucjS3b//a3CmMGgwFTp05FcnIyNm3adMPjZrMZ9957LwICApCSkoLy8nI8+uijEIvFeP311xkkJuR6crkcI0aMwIgRI8BxHEpKSpCSkoLU1FT861//wrZt29DS0oKkpCT4+fkhOjoa0dHRiIqKgpubG+v4XcJsNiM3N9dalidPnkRVVRWEQiHi4uJw9913Y8iQIRgyZAh8fHxYxyXEymFGnq22bNmCZ5999oaR508//YT77rsPZWVl8Pf3BwB88skn+Mc//oGqqqp2T9igkSdhQa/XIysrC5mZmcjJyUFWVhaKiopgsVgAAIGBgdeVaXR0NCIiIhxiIhLHcaiurkZRUZH1VlxcDJ1Oh7Nnz6KsrAwuLi5ISEjAkCFDkJiYiEGDBkGhULCOTnjGKUeefyY1NRX9+vWzFicAjB8/Hk888QQuXryIAQMGtPnn9Ho99Hq99WuNRtPlWQn5I6lUigEDBlz3PjUYDMjPz0dubi7y8vKQm5uLn376CRUVFQAAoVCI0NBQREdHo0+fPvDx8YGnpyeUSiU8PDygVCqhVCptOmxxu4xGI0pKSqzF+PuSLC4uRktLi/V7VSoVQkJCEBcXhzlz5iAhIQHx8fGQyWRdnpOQzuI05VlRUXFdcQKwft26sWnLunXr8PLLL3dpNkJuh0QiQc+ePdGzZ8/r7m9ubraWaWuxpqSkoK6uDpcvX77heeRyOTw8PKyF+sf/KpVKyGQy6PV66HQ66wfK1q8NBsMt7/fz88Nvv/1mHSW7uLggODgYoaGhSExMxEMPPYTQ0FCEhIQgNDSUVvUhToFpeb7wwgtYv379Lb/n0qVLXXpZoOXLl2PJkiXWrzUaDZ1KQOyam5sb4uPjER8ff939er0eDQ0N0Gg01/23rfvKy8utj+l0OkRGRuLChQuQSqWQSCSQyWSQSqXWm0wms97v7u4OHx8f6/2BgYEYN26ctSADAgJo3V/i9JiW59KlSzF37txbfk9kZGS7nisgIAAnT5687j61Wm197GZaNw6EODqpVAo/Pz+brwxiNpthNpshFotpVSRC2olpeapUqk6bbp6cnIy1a9eisrLSuvHYv38/lEol4uLiOuVnEOKMRCIRjRQJsZHDHPMsKipCbW0tioqKYDabkZGRAeDauV/u7u4YN24c4uLiMHv2bLz55puoqKjAihUr8NRTT9HIkhBCSKdymFNV5s6di61bt95w/+HDhzFq1CgA1y5w+8QTT+DIkSNwc3PDnDlz8MYbb9AiCYQQQv6UU64w1F2oPAkhhJ9s2f7zdx0wQggh5DZReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMqT0IIIcRGVJ6EEEKIjag8CSGEEBtReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMqT0IIIcRGVJ6EEEKIjag8CSGEEBtReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMqT0IIIcRGVJ6EEEKIjag8CSGEEBtReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMqT0IIIcRGVJ6EEEKIjag8CSGEEBtReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMX1gHsDcdxAACNRsM4CSGEkO7Uut1v7YFbofL8g8bGRgBASEgI4ySEEEJYaGxshIeHxy2/R8C1p2J5xGKxoKysDAqFAgKBgHUcaDQahISEoLi4GEqlknUch0Gv2+2h18129JrdHnt83TiOQ2NjI4KCgiAU3vqoJo08/0AoFCI4OJh1jBsolUq7eYM5Enrdbg+9braj1+z22Nvr9mcjzlY0YYgQQgixEZUnIYQQYiMqTzsnlUqxevVqSKVS1lEcCr1ut4deN9vRa3Z7HP11owlDhBBCiI1o5EkIIYTYiMqTEEIIsRGVJyGEEGIjKk9CCCHERlSedmzt2rUYNmwY5HI5PD092/yeoqIi3HvvvZDL5fDz88Pzzz8Pk8nUvUHtXHh4OAQCwXW3N954g3Usu/Phhx8iPDwcMpkMSUlJOHnyJOtIdm3NmjU3vK969erFOpbdOXr0KCZNmoSgoCAIBALs3r37usc5jsOqVasQGBgIV1dXjB07Fjk5OWzC2oDK044ZDAZMnToVTzzxRJuPm81m3HvvvTAYDEhJScHWrVuxZcsWrFq1qpuT2r9XXnkF5eXl1tvTTz/NOpJd2blzJ5YsWYLVq1fjzJkz6N+/P8aPH4/KykrW0exanz59rntfHTt2jHUku9Pc3Iz+/fvjww8/bPPxN998E++99x4++eQTpKWlwc3NDePHj4dOp+vmpDbiiN3bvHkz5+HhccP9e/fu5YRCIVdRUWG97+OPP+aUSiWn1+u7MaF9CwsL49555x3WMexaYmIi99RTT1m/NpvNXFBQELdu3TqGqezb6tWruf79+7OO4VAAcN9//731a4vFwgUEBHD/7//9P+t99fX1nFQq5bZv384gYfvRyNOBpaamol+/fvD397feN378eGg0Gly8eJFhMvvzxhtvwMfHBwMGDMD/+3//j3Zt/47BYEB6ejrGjh1rvU8oFGLs2LFITU1lmMz+5eTkICgoCJGRkZg1axaKiopYR3Io+fn5qKiouO695+HhgaSkJLt/79HC8A6soqLiuuIEYP26oqKCRSS79Mwzz2DgwIHw9vZGSkoKli9fjvLycmzYsIF1NLtQXV0Ns9nc5nvp8uXLjFLZv6SkJGzZsgU9e/ZEeXk5Xn75ZYwYMQIXLlyAQqFgHc8htG6n2nrv2fs2jEae3eyFF164YZLBH2+0wfpztryOS5YswahRoxAfH4+//e1vePvtt/H+++9Dr9cz/i2II5swYQKmTp2K+Ph4jB8/Hnv37kV9fT2++eYb1tFIN6CRZzdbunQp5s6de8vviYyMbNdzBQQE3DAjUq1WWx9zZh15HZOSkmAymVBQUICePXt2QTrH4uvrC5FIZH3vtFKr1U7/PupMnp6eiI2NRW5uLusoDqP1/aVWqxEYGGi9X61WIyEhgVGq9qHy7GYqlQoqlapTnis5ORlr165FZWUl/Pz8AAD79++HUqlEXFxcp/wMe9WR1zEjIwNCodD6mvGdRCLBoEGDcPDgQUyZMgXAtYvCHzx4EIsWLWIbzoE0NTUhLy8Ps2fPZh3FYURERCAgIAAHDx60lqVGo0FaWtpNzzKwF1SedqyoqAi1tbUoKiqC2WxGRkYGACA6Ohru7u4YN24c4uLiMHv2bLz55puoqKjAihUr8NRTTznslQo6W2pqKtLS0jB69GgoFAqkpqZi8eLFeOSRR+Dl5cU6nt1YsmQJ5syZg8GDByMxMRHvvvsumpubMW/ePNbR7NZzzz2HSZMmISwsDGVlZVi9ejVEIhFmzJjBOppdaWpqum40np+fj4yMDHh7eyM0NBTPPvssXnvtNcTExCAiIgIrV65EUFCQ9YOc3WI93Zfc3Jw5czgAN9wOHz5s/Z6CggJuwoQJnKurK+fr68stXbqUMxqN7ELbmfT0dC4pKYnz8PDgZDIZ17t3b+7111/ndDod62h25/333+dCQ0M5iUTCJSYmcidOnGAdya5NmzaNCwwM5CQSCdejRw9u2rRpXG5uLutYdufw4cNtbsfmzJnDcdy101VWrlzJ+fv7c1KplBszZgx35coVtqHbgS5JRgghhNiIZtsSQgghNqLyJIQQQmxE5UkIIYTYiMqTEEIIsRGVJyGEEGIjKk9CCCHERlSehBBCiI2oPAnhkYKCAuvC+V25dmh4eLj159TX13fZzyGEFSpPQnjowIEDOHjw4A33l5SUQCKRoG/fvjc81lq8rctE/t6oUaPw7LPPWr8+deoU/v3vf3dmZELsCpUnITzk4+MDHx+fG+7fsmULHn74Yevi3LdLpVLB29u7IxEJsWtUnoQ4qKqqKgQEBOD111+33peSkgKJRNLmqPLPcByHzZs3Y/bs2Zg5cyY2bdrUmXEJcSpUnoQ4KJVKhc8//xxr1qzB6dOn0djYiNmzZ2PRokUYM2aMzc93+PBhaLVajB07Fo888gh27NiB5ubmLkhOiOOj8iTEgU2cOBELFy7ErFmz8Le//Q1ubm5Yt27dbT3Xpk2bMH36dIhEIvTt2xeRkZHYtWtXJycmxDlQeRLi4N566y2YTCbs2rULX3311W1dy7W+vh7fffcdHnnkEet9jzzyCO26JeQm6GLYhDi4vLw8lJWVwWKxoKCgAP369bP5Ob7++mvodDokJSVZ7+M4DhaLBdnZ2YiNjYVSqQQANDQ03PDn6+vr4eHhcfu/BCEOhkaehDgwg8GARx55BNOmTcOrr76Kxx57DJWVlTY/z6ZNm7B06VJkZGRYb5mZmRgxYgQ+//xzAIC3tzd8fX2Rnp5+3Z/VaDTIzc1FbGxsp/xOhDgCGnkS4sBeeuklNDQ04L333oO7uzv27t2L+fPn44cffmj3c2RkZODMmTP46quv0KtXr+semzFjBl555RW89tprcHFxwZIlS/D666/D398fQ4cORU1NDV599VWoVCo8+OCDnf3rEWK3aORJiIM6cuQI3n33XWzbtg1KpRJCoRDbtm3Db7/9ho8//rjdz7Np0ybExcXdUJwA8MADD6CyshJ79+4FACxbtgyrV6/G+vXrER8fj4ceeghubm44fPgwXF1dO+13I8TeCTiO41iHIIR0j4KCAkRERODs2bNdujwfcK3cR48ejbq6Onh6enbpzyKku9HIkxAeGjZsGIYNG9Zlz9+nTx9MmDChy56fENZo5EkIj5hMJhQUFAAApFIpQkJCuuTnFBYWwmg0AgAiIyMhFNLndOJcqDwJIYQQG9HHQUIIIcRGVJ6EEEKIjag8CSGEEBtReRJCCCE2ovIkhBBCbETlSQghhNiIypMQQgixEZUnIYQQYiMqT0IIIcRG/x+WOgRqiZd92QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = rebound.OrbitPlot(sim, unitlabel=\"[AU]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Integration with IAS15**\n",
    "\n",
    "We will integrate backwards in time for 70 years. Because we don't know what will happen yet (hint: a close encounter) we will use the IAS15 integrator. It is fast, accurate and has adaptive timesteps to capture any potential close encounters. \n",
    "\n",
    "To integrate backwards, we could set a negative timestep or multiply all velocities with $-1$. We'll choose the first option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.dt = -0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While we're integrating, let's store the positions of Jupiter and the comet at 10000 times during the interval. We'll need to prepare a few variables to do that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "Noutputs = 10000\n",
    "year = 2.*np.pi # One year in units where G=1\n",
    "times = np.linspace(0.,-70.*year, Noutputs)\n",
    "x = np.zeros((2,Noutputs))\n",
    "y = np.zeros((2,Noutputs))\n",
    "z = np.zeros((2,Noutputs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're ready to start the integration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.integrator = \"ias15\" # IAS15 is the default integrator, so we actually don't need this line\n",
    "sim.move_to_com()        # We always move to the center of momentum frame before an integration\n",
    "ps = sim.particles       # ps is now an array of pointers and will change as the simulation runs\n",
    "\n",
    "for i,time in enumerate(times):\n",
    "    sim.integrate(time)\n",
    "    x[0][i] = ps[1].x   # This stores the data which allows us to plot it later\n",
    "    y[0][i] = ps[1].y\n",
    "    z[0][i] = ps[1].z\n",
    "    x[1][i] = ps[3].x\n",
    "    y[1][i] = ps[3].y\n",
    "    z[1][i] = ps[3].z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Visualization with matplotlib**\n",
    "\n",
    "Let's plot the orbits of Jupiter (blue) and the comet (green) to get an idea of what was going on during our integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ggxdrG63X/HSHRJEoByU6EUTcSUR6tla/fnxqV2g0NPiEEMLP9Itw49k0ErM0KNEJTKfj8MbyCP36/1oGoIq3u4QREULsnUajwZU5PfTrKZm5OB39VMKI5I0SncBMr8t9+XoTiSIhhMhJWVcnzO3fUL8+YOkJcBz1sCsJSnQCmvLXBaN1ui5HCCmOYS9UN1oPnkY97EqCEp1AUjJzsDHygX59+/sd6LocIaTYTL8gf7P7ukSRyBclOoE0nr3baL1+FeotRwgpPo1Gg4MFOh0s3n8LmTlay08gZijRCaBt+D6jdSrWTAgpjaAKZRHiV1a/Xvcz6l9XHJTobCwxLQsPkzP169R2hxBiC/undDZan7rxojSByBAlOhtrMc/QX65xgBfKUx1LIgSOA7S5gI6qZqjJmRlh+uV1p2OQnUv//kXhJHUASvLKT8eM1v+d0F6iSIhsZKYAKQ+B1IfsPuURkBILZDxlj2WlAJnJbDk7DdDlshtX4ANO4wg4uQKOLuze1RNw9wbcvAF3H6CML+BZJe9W1XDvSP/95aZCOVc0CfDChQfJAIDaM3bQpZEioL90G8nI1uLc/ST9+jk6ZUnycRyQdA94fB14cgN4cjPvdgN4/sQGr68Fcp6zGwCkxRf+HEcXwCcYqFAL8K0J+NUBKjcBKtShBGjn/pnQ3qiNz89H7uCdDiESRmT/6C/aRuoVqGXp6eZErXfULPkB8PCc8S3jmeX93bzYEZZHZcORV5kKgJsne8zVky27lAMcnQEHJ3bT5F15yM0CtNnslpvJjgAzkoDMJPa+6Y8NR4opsezIUZsNPLnObgU5uQH+9VnSqxYKVG8DeFcHaGqMXYmY1g0v5A16m7ftGka2D6bpS1ZQorOBP0/dN1q/OLuHhT2JIiXdB+4eAaKPslvyffN9HJzZUVOFWoBvLaBC7bzlGoCrh7jx6nRAygN2VJl4i90nXAPiLrJTpQ8j2e3sb2x/jypA9bZAcAegZhjgFSBuvMRMJS83o/XgadvpFKYVGs6Oa8qkpKTAy8sLycnJ8PS033loBU8j/DehPRoFeEkYDRFcdjpw5yBwYye7TzJJbBpHoGJ9oEozw82/Prt+Zs90OuDZXeDRBZbo7kewo1FdrvF+fnVZwqvVHajejk51SoTjOKNKKQc/7IygCmWtPEPeSpMPKNGVkmnLe/pWpVDJscCNHcD1ncDdw4A2y/CYxhGo2hwI6gAEtWen/FzLSRerLWWnAw/OAPeOA3cOAA9OGw+EcS8P1HsJqN8fCO7ITq0S0Wy/9AjvronUryv584cSnUSSM3LQZI6hAsrtBb3h6EDnyRUj7TFwdQtw6W8gJsL4Ma9AoE5PdlQT+IL4px+l8vwpO4q9tZcd0T4v0AHb3Qdo+BrQdAg7iqVrRqIo+GV7VIdgfNqnvoTRCIcSnUQK/oF1r18Ry99sKWE0xCay0oBr/wKXNgB3DrERjQAADVCtNVC7J7v516MPcm0ucO8ocGULcO0/4xGk/vWBpoOBJoOBsr6ShagGz7NzUX+moV/d3fDeihyYQolOAsduPcGQn0/q15V8ykAVHp4Dzq5iCS47zbC9SjOg4etAw1fZaEjCT5sL3D0EnF8DXNtqOLXr6Ao0HgCEjgMqNbT+GqTE1HAJhRKdBAr+Ya0b/QJeCKFvrbKTlQZcXA9ErmIDMPKVDwGaDGKn4XxrSBefXGUkAZc3AmdXspGc+YI6AKFjgTq9AAdHqaJTJNOBKVFze8LNWVm/Y0p0Ipv5z2X8fuKefl2J354ULTkWOLUMOLMSyGIVJuDoAtTrC7QYzgaUKPDUj+g4Dog5CUQsYac2808DV6gDdPyIHSVTwrOZ8O3XsOzwHf260j6XKNGJrODR3IWZ3eFVhkaayUJsJBDxE3Bls2HIvG9NoOVIoMkbQJny0sanZMkPgNO/AGd+YRPaAfa77/gROzVMUxRsouBn09FPuiDAp4yE0dgWJToRtZi7B4np2fp1pX1rUqR7J4BDC9lowXxBHYA2E9ioSQeqbS6azBTg1HLgxA+GajHlQ4Bus4D6/ehIupSO3nyCob8oc+xAafIBfY0qBo7jjJLczfm9JIyGFCr6KHBwIRB9hK07OLHrbi+8C1RpKmloquXmCXT8EAgdA5z+GTi+GHh6B9jwFlDtBaDHfCCARi+XVPtaFYzWI+8/Q/NAH4misR90RFcMahjZpAgxp4B9nxdIcM5AsyFA+8mAT3VpYyPGstKA44uAY4uA3Ay2rcGrQNhs+rcqoVsJaQj79pB+XSmfU6XJB3TOpohMvw/cWdBbokiIRYm3gfXDgF9eZEnOwRlo+Tbw/jng5f+jD0575FoO6DIdeD8SaDoUgAa4sgn4MRQ49n+ANkfqCGWnpr9xVZ5jt2zQIUPmKNEVUcGhuwDgQBVQ7EfaY2Dbh8CPrdlkb40D0GwYMPE88NJ3gHc1qSMkhfGsAvT/ERhzmNXPzM0A9swElncGYk5LHZ3sREzrpl8uON9XrSjRFYHp0dzdcDqaswvaHODEj8CiZsDpFWwkZa0ewNhjQL8fqMq+HFVuDAzfBvT7idXRjL/MjtC3TWGnOUmRmHY3OHkn0cKe6kCJrghMj+aUWF5HdqKPAcs6ArumA9mpQOWmwFv/AUP+Yp0DiHxpNOya6oQzrG4mODZwZWl7dv2VFEnBo7qByyOs7Kl8lOiKia7NSSw1Dtg4CljZG0i4yr71v7wIGHWAVc8nylHWF+j/E/Dmv4BnAGsh9GsPYN9cIDe78OernOlR3c34VIkikZ6giS48PBytWrWCh4cH/P390b9/f1y/fr3wJ9qRPouOGK3TtTmJcBwQuRr4oTVw6S8AGjbQ5L2zQIu3aC6ckoV0AsYdAxq/wVoEHfka+CWMDT4iVu2b0km//OJ3hyWMRFqCfjocOnQI48ePR0REBPbs2YOcnBx0794d6enpQr6tTV15mKJfvk1Hc9J4dg9Y/Qrw7wRWsqtKM2DUfjbQhKqZqIO7N/DqMmDAStYO6NEFNlDl6r8SB2bfavgZj8BMzlDnKFZR59E9fvwY/v7+OHToEDp2LPw0k9Tz6L7fewPf772pX1fKfBTZ0OnYtZm9s4GcdMDJDejyKZvwTSWj1CvlIfD328D9E2y9zQQ2746avvI6cvMxhv1iuLYp188x2cyjS05mNe7Kl5fHt/CCSe7ynB4SRqJCKQ+BP14BdnzEklxgW2DccaDd+5Tk1M6zCht41GYCWz/xA7DqZSA1Xtq47FSHWn5G6zqd3dYIEYxoiU6n02HSpElo164dGjbk70uVlZWFlJQUo5tUbphcuC3nSh+uorn6L7CkLatN6eQO9P6aDTmnljkkn6MzKxf2v9WAqyc7uvu5GxB/RerI7NKwFwzFEurO3ClhJNIQLdGNHz8ely9fxrp16yzuEx4eDi8vL/2tWjXpJvp2L3Dhdut77SWLQ1Wy0oB/JgB/DWMFfys3YROIW4+iwSaEX/2+bMStb00gOQb4pTtwY7fUUdmdz/s10C9n5+okjEQaonx6TJgwAVu3bsWBAwcQEGB5Eu+0adOQnJysv8XExIgRnhnTQ/uGVb0kiUNVEq4BK7oA51YD0ADtPwBG7gX8aksdGbF3FWoCI/ewjhTZacCfA4GIpVJHZVdM5/7+EXHPwp7KJGii4zgOEyZMwObNm7F//34EBwdb3d/V1RWenp5GNymETDdMEH+1eVVJYlCVi38BK7oCT24AHpXZ9Zew2YCTi9SREbkoUx4YuomVfuN0wM5P2CAm+61ZL7ob8wzdVmZsuSxhJOIT9MLT+PHjsXbtWvzzzz/w8PBAXFwcAMDLywvu7u5CvrXNfDOgidQhKFdOJrBrGnDmV7Ye0hl49WegnJ/VpxHCy8kF6LuYXcvdOxs4+h2QkQT0+YY6mQNwcTI+rknNzIGHmzpGqgp6RLdkyRIkJyejc+fOqFy5sv62fv16Id+2VLZfemS0TuW+BJIax6qbnPkVgAbo9An7Rk5JjpSGJu+098uLAGiAs78BG9+hSip51o4K1S83mq2ea5mCHtHZcas7i95dE6lfjvzsRQkjUbCH54A/BwOpD9nk31d/BmqFSR0VUZIWb7EmrxtHsbY/2WnAwD8AJ1epI5NU2xoVCt9JgWgoWwGmibl8WbpGZHOXNwG/9mJJzq8uq3BCSY4IocErwOB1bIrKzd3AX2/RkZ2Jv88+kDoEUVCiK6DxHMOhfP+mVSSMRIF0OuBAOPD3CNZrrFZ3NlKufIjUkRElqxmWl+zcgBs7gI1vq76Za8FBKR9uuCBhJOKhRFdAamaufvm7gU2lC0RpcrOBzaOBQwvZepsJwKB17NQSIUIL6Qy8sQZwdAGu/QdsGgVocwt9mlKZDkpRQ6UUSnR5EtOyjNZpEIqNZKUCa/8HXNoAODgB/X5kFS1oFBwRU80wdo3OwRm4shnYNlnVUw8+7G6Yn/rGCuX3qqNEl6fFvL365bXvhFrZkxRZ2mNg5UvAnQOAc1lg8Hqg2VCpoyJqVbsH8PqvgMYBiFwFHPpS6ogkM75LTf3yqbtPJYxEHJToeLStqc6RSTb19A7wy4vAo/NAGV9g+H/sWzUhUqrfF+j9FVs+uACI/F3aeCRiesYqK1crUSTioEQHIObpc6lDUJaEKOCXHqwjtHd1NuikagupoyKEafUO0OFDtvzfJNXWxlw5opV+ubHC59RRogPQ4csD+uX9BTrykhKIuwys7AOkJwAVG7IkR10HiL3pOgNoMhjgtKy3XUKU1BGJrnMdf/1ylsILPVOiMxFi0pGXFMPD88Cql4DnT4DKTVnNSo+KUkdFiDmNBui7CKjeDshOBdYNYh0zVEzJpy9Vn+jiUzKlDkEZYs8Cv/dlHxZVWwBv/sMK7RJirxydgf/9DngFsmvKf7+tumkHvw5vqV8u2JpMaVSf6EIX7NMvU9+5EoqNBH7vD2QmA9VCgWGbAXdvqaMipHBlKwCD1gLOZYDb+4F9s6WOSFRd6xrOuNxLVO5YBWqbXQD1nSuB+KvAH68CWSlAYFtgyF+Aq4fUUUkrJ5Md2WYmAWnxQMpDIOc5kJvFbrpc9sFa1o990Lp7Ay7lgHL+gJs3O61GxFOpEdB/CbDhLeD4YnY6s06vwp+nQBzHKXIOsaoTnVYFFQEElXgbWN3fcLpSLUmO44C0BOD+ceDKFuDqFuHeq+FrQP1+QJVmgFc1SoJCadAfuD8OOLkE2DIOGHsU8LLcJFpJPgirje/23gAAfL37Oj7qUVfiiGxPw9lxi4GUlBR4eXkhOTlZkCas3b87hBvxaQCAz16qj5HtrTeGJQUkxwK/9gSS7wP+DYDhW5V7TS4tAbj6D7B/HjtKk1r19kD7SUBgG8CVBk/ZTG428Gt31l2jWigwfBu7jqdwHMcheJqh2XT0wj4SRmNZafKBqo/o8pMcAIxoGyRdIHKT/oQdySXfZ0WZh21WVpJ7/pT1yds/V+pI+N07ym75GrwCdPwY8K9HR3yl4eQCvP4bsKwjEHMSOBgOdJspdVSCU+KpSlOqTnQFOTgo/x/bJnIygD/fAJ7cADwD2OhKJUwhiL8CbB4DxF2SOpLiu7KZ3QCgQm3glaVAleaU9EqifDCbdrBhOOtQXrsXUK1VoU9TktikDFT1dpc6DJtSbaK7EZ8qdQjyo9Oybs0PTrNBE8M2Ad6BUkdVcjGnWcHpDBvX+nP3YQNzfGuwD06fYDboxMEp7+bIrvOlPAQSb7HkGneR/V5L68kNYEVXttxqFNB5GlDWt/SvqyYNXgGu7wAurge2jAXGHAFcykgdlaBOTu+mH4HebuF+uz19WVKqTXQF54xETOsmYSQysnsGELWVtTt5Yy3gV0fqiIov7TGwcSRw91DpXselHNBoQN5AkaYsuRWXbw0guIPlx9MTgQengHN/sN97cZ1ewW4AMOoAULV58V9DrXp9Adw9zL6I7JvD1hWsoqeb1CEISrWJrqBKXsr+R7aJiCVAxE9suf8SIKidtPEUB8cB51YD/75X8teo0wdoPQoIfAFwFum0TllfNsw9f6i7TgfEX2bdsot7/XBFF3Y/aD2r4k+nNa1z9wH6/gCseQ04uRSo9zIQRPNs5YoSHSncjd3AzmlsOWwO0Oh1aeMpqux0YNPokh0N+ddnAxFCugDOdvJFyMEBqNyY3Tp+yAbNXN8ORK4GYorYU+zPgex+0HqgTk/hYlWCWmFA8zdZh4OtH7ApB06uUkclmJbVfXDmHiuDdvFBEhoHeEsbkA2pcnrByTuJGLicfTBUKOeCMzNetNlrK86Tm+yaT1YK0GI48NL39n80kBwLfFe/+M+r3RMIm81GL8pNWgJwYR076k59VPTnjT3KJkwTfhnPgB9aAemPgS4zgE4fSR2RYNKyctFw1i79ur1dpytNPlBlCbD8JAcAOyd1lDASO5eZDPw5KK/qSRug11f2neSe3gVmexUvyVVqBIw7DsxOZo1h5ZjkAFZVpd37wORrwFtbWdIuiqXtgYXV2bVLYs7dB+gRzpYPf8WKJChUOVflnuBTZaIrqEI55Z6KKBWdFtg4Cki8CXhWZcVvnVykjorf0zsswS1qWvTn9F8CzHjMjmgqNhAsNNFpNGyAy+D1wPhTQNMhhT8nMwn4uiZwchm7nkmMNXodCOkMaLOA7R/R70iGVJ/oiAUHFgA3dwFObsAba9gRg715/jQvwTUr2v4VGwETL7Cjt6aD7Tdx24pfHaD/T8CEs2yEaGF2fAzM8QaS7gsemqxoNECfb9lo49v7gJt7pI5IMC6OhpTwND1bwkhsS3WJLj1LXW04SuTmXuDI12z55UWszqI9yc0Cfn4R+LKIJdtavQNMvQ+MOwr4BAkaml2qUBN47WdgzGE2v68w3zdiR3fEwLcGEDqWLe/+FNDmSBuPQPZ/aGg8PeTnkxJGYluqS3Sv/nRcv/zXmDYSRmKnkmOBzaPZcqt3gCYDpY3HVMQSYJ4/m19WmM7Tgc+eAH2+AdyoMwUqNwFGbAde/xUoV8n6vjs+BsID2chVwnT8ECjjyybln10pdTSCCPAxTIy/9ihFwkhsS3WJ7nqBiigtq5dgkq+SaXPZZOrniUClxkD3+VJHZJAQxU5T7pxa+L5dZrAE1/kTVRTlLRaNhnVEGH8SaDbM+r5ZycCCKqw8GmFflrpMZ8sHFgAZSZKGQ4pOdYmuIKpvaeLgAuD+CcDFAxiw0j7mj+m0wHeNgJ9CC9/3hXfZAJNOH1GCK4y7N9DvB2DYFsCjsvV9l7Q11NJUu+bDgQp1WNm4/AIKxO6pOtGRAu4cAo58w5b7LmLXJKQWfRT4vDzrkmBNYBvgk2igZ7jyB5jYWo0uwNhjrHixNRuGsxJwah9x6OhkOKo78RMbEKUw7WoaaqPGPFVG13FVJbrMHK3UIdinjCTWbBJgk8IbviplNOxC/2wvYGURJqy+Fwm8vbNktSYJU9YXGPQn0GMBoHG0vN/xxcDyzuwUt5rV68tG8Ganst+Jwnw/0DD4bMRKGxQatwOqSnQT153TL699pwinwtRi+0dASizrLddjgbSx3D0MzK1Q+H79lwCzkuzjyFMJNBqgzXjWkcLdSm/BR+fZv0+ucoaeF5uDA9AlryTeyWWsP6OC+HkY5hbfSkizsqd8qCrR7boSr19uFaygRqGlcXkjcOkvQOMAvLIccCkrTRwcB3zbAFj1svX9gjoA02LZPDh7rtIiVyGdgdEHAN9aVnbigHl+bJqHWtXpDVRuCuSkA8f+T+poSCFUlegKcnZU7Y9ukPIQ2DqZLXf4ULoGk6lxbKJyygPr+43YAQzfCriWEyUs1fIJAkbuBgIK+XuY588a8aqRRsN6/QHAmd9YuTxit+jTXq04jiW5zCT2zbTTx9LEcehL4JtC+toFdQCmPwKqF2GyM7GNMuWBN/8FanW3vt/8Suo9jVmrO+BXl12rO7tK6mgEY8d1/4uMEp1aXd0C3NgBODiz611iD8fnODbg5EAhc/WGbmRHcQrv8GyXXMoAA/8ofETmN7VZrzy1cXAA2kxgyxFLFJXwezcyFBS48lD+E8dVk+iyc1X4H9GS50/ZABQA6DAZqFiCljalkfaYnaq0xsmdle2qGSZKSMQCJ1dW0LuOlRGwGc+A1f3Ei8meNP4fUNYfSH2oqLmGc/o21C+/rYCRl6pJdD8euKVfXjashYSR2IHdn7H+WhXqAB2miPvel/5mlfKt6fAh8OkjKttlL5xcWNmwoA6W97l7GNgzU7yY7IWTKxA6hi2fWKyYeYYFR14mpMp/0JFqEt3/7bupX25Tw9fKngp35xBw/g8AGqDvYnE7Jq8fxkqMWTNqP9DtMxpRaW+c3YA31rLruZYc+z/g+k7RQrIbLd9mXT7iLgEPzkgdDeGhmkRXkKebSstDaXMMpyxbvQMEijSXMH8C+LV/re/3yT2gqsqPtu2Zmycw+C/Wn9CSPwey/oBqUqY80OAVtqzQYs9yp8pEp1qnlgNPrgNlKgBdZ4jznulPCp8AXrsnMPMpq79I7JtHRdaf0MlKHdRFzYAsZUw0LrIWw9n95Y1U7NkOUaJTi9R44OBCthw2S5yk8vgG8FUhlUt6f826YTtYKT1F7EuVZkC/H63v82NrcWKxF9VCAb96QG4GcGmD1NEQE5To1GLvbCArBajSHGg6VPj3u3sE+LGQCcdv7wZajxI+FmJ7jV4H2k2y/HhKLHB+rWjhSE6jMRzVKfD0pdwbVlOiU4OY08CFvA+d3l+x+T9COr8WWPWS9X3ePy/eNUIijK4zrF9T3TIOSIoRLx6pNRkIOLoA8ZcV0cNvyou19cunouXdpUEViU6nU8aQ3xLhOGBXXluRpkOBgJbCvte+zw2dECz56A5QPli4OIg4HJ2BV1cALlZKsn3fUD2Tyd19DJVkFHD68tUWAfrlZYduSxhJ6aki0V2MNdShe69rIXO4lCZqG/DgFOBchg3bFwrHAVsnGXra8dE4sFJeZVU8vUNpfGsAvb5kyw5O/Puc+EG8eKTW6HV2f2mj7BN8VW93/XLEHTqis3trIu7pl19qXEXCSESmzWVHWADrvu1Ryfr+JaXTAptGW7824VEZmJFApbyUqOlgoO5LgC4X8K5u/viez1jhbjWo3ZMd4SbfZ18wiV1QRaLbcNZQFb+qj7uVPRXmwlo2ncC9PNDufWHeQ5sD/PUma/VjiX8D4IMr4tfTJOLQaNhRnUs5IOke/6nMb0UuMycVZ3egXl6rqUt/SxsL0VNFoiuorItKhrFnPwcOhLPljh8KU04rNxtYOxCI2mp5n8A2wNijNH1A6byqAl3yrgXzfaHhtMDNPeLGJJUGr7L7qK2KKQkmd6pLdBq1lJY6/TMrNOsVyKqg2Jo2B/hrGHB7n+V9AtuwHnJCj/Ik9qH1GKBiI1bkma8u5prX2el0pQvuCDiXBVIfsY7sRHL0CaRE2c+B44vYcudPbF/PUpvLalbesFLXsFIjYPh2qlmpJo5ObPoKANw7zn8K89RycWOSgrMbULMrW76+Q9pYCABKdMp0diXrTuAdCDQeaNvX1mnZ9IGr/1jexycYGH2IjuTUqHoboE5vdqqS76hu1zQgK1X8uMRWpze7v75d2jgIAEp0ypOTyarIA0D7ybYdAKLTAf++b33gibsPMOE0XZNTs24z2VSSGzuAkM7mj+ePBFayWt3Z7yDukromzdspSnRKc241kBYHeAawYd+2tHdWXosfK6Zcp9GVaudfD2gyiC1reD5iTi0HMuXftdqqshWAqnnFGe4ckDYWQolOUXKzgaPfs+X2k2x7be7Ej4brfpZMjRG3vx2xX50+BjSOwO39QCueeqaHvhA/JrGFdGL3dw9LGwcRJ9H9+OOPCAoKgpubG0JDQ3HqFE2kFMSVTUDKA6BcRaDZMNu97qW/DWXELJkcxfqVEQIAPkGGHm0ZPFU1Tvyg/FY+wQUSHU0zkJTgiW79+vWYPHkyZs2ahcjISDRp0gQ9evRAQkKC0G+tLhzHjroAoPVoNvLLFu4cLLwr+LgTgGdl27wfUY52E9n9lc1Ahw/NHz+9Qtx4xBbQivXtS4sHHl+XOhpVEzzRffvttxg1ahRGjBiB+vXrY+nSpShTpgx+/fVXod9aXe4dA+IuAk7uQMu3bfOaT24C69+0vs/QjUBFlVS9IMVTuTFQoxvA6YDsdPPH986WfT1Iq5zdgMAX2PLdQ9LGYgOcjI9KBU102dnZOHv2LMLCwgxv6OCAsLAwnDhxwmz/rKwspKSkGN1IEeUfzTUdBJQpX/rXe/6UVT3JSra8T5cZQM0wy48T8sK77P7Cn2xCuambu8WNR2xB7dn9/Qhp47ABOTeBETTRPXnyBFqtFhUrVjTaXrFiRcTFmRd5DQ8Ph5eXl/5WrVo1IcNTjsTbhomp+R8spaHNATYMB55aac0R2Abo9FHp34soW40urDpPZhLrTG7qTxvP87Q3AXmd1h+ckTYOG8iV8dG3XY26nDZtGpKTk/W3mBiaf1Ikp5YD4IBaPYAKtUr/ejunFn6q5c1/S/8+RPkcHIHmeae/I383DLkv6OldcWMSU9XmADSsm0FqvNTRFJuzo6GykVbGh3SCJroKFSrA0dER8fHG/8Dx8fGoVMm8ZYyrqys8PT2NbqQQORnstBDABqGU1tmVrE6mNR/eApxcSv9eRB2aDWFTDe4fB3osMH88/7S7Erl6AP5517Bj5XdUl6M1JDcZX6ITNtG5uLigRYsW2LfPUPhXp9Nh3759aNOmjZBvrR5X/wEyk9npoRpdS/daD88D2ws5Hfn2LqCcX+neh6iLZxV2ChPgP1NweoWyB6UEtGD3MfKeVuXkKN+6tYKfupw8eTJWrFiBVatW4dq1axg3bhzS09MxYsQIod9aHfKbnbZ4s3S1JTOesb5y2mzL+7SbaBhFRkhx5LeuubwJ6MkzWTz6iLjxiKlqXqJ7dEHaOErJWca1a52EfoOBAwfi8ePHmDlzJuLi4tC0aVPs3LnTbIAKKYGEKOD+CXZaqOnQkr8OxwFb3mVNMy1x8wLC5pT8PYi61e0DbHUBHl9jbWxMHVhgqCSiNBUbsvuEq9LGUUoODnREZ9WECRNw7949ZGVl4eTJkwgNDRXjbZUvchW7r92zdBO2jy8qvMr6xAvUcoeUnLu3YSrK1X8AB5N6qDERrDOGEvnVZfdp8UD6E2ljUSn5HouqnTYHuJjXRaB5IZO6rXlwFthbyJHaW1tZVwJCSqNuH3Z/czcw4Dfzx2V+Dcsi13KsdRUAxF+RNhaVokQnV3cOAs+fAGV8gZrdSvYaWWnAplGsd5gl9V4Ggnn6ihFSXPlHdA8jgWo813ojFDz6smIDdi/z05dyRYlOrvKP5hq8WvK2OLs/tT4pHABe+6Vkr02IKY9KrPM8ANzeZ/74tf/kPYbdGv967J5qXkqCEp0cZacDUdvYcuP/lew1orYZRmxaMu44td0htlWrO7u/tY9/9GViIV+85Cr/1OUzBU+Ot2OU6OQoajuQk85aoQS0Kv7z0x4D/75nfZ8X3jWcbiHEVvJHXN47zl98/PZ+ceMRS/n8RBctaRhqRYlOji5vZPeNBpRsJOSOj4Dnidb36T6v+K9LSGECWgEOTqxvYpp5vVvsUGj9VJ8gdp8UwwaSEVFRopObrDTDt976/Yv//GtbWX8wa8YcZjUKCbE1l7JA5SZs+d4J/kEpSpxmUK4S603HaYFkquErNtUlOjkXJgXALuJrs9g3xOKeWsxIArZNsb5Pvb6GDyJChBCYV/4v5iTwIs/UlriL4sYjBgcHw1GdkotY2ynVJbpnz62UuJKDa1vZfd2Xin/acvcM/tNFBb2yrGRxEVJU+e164i4B1XiKR8ScFjcesXgFsPvUR9LGoUKqSHRjOoXol2OfZUgYSSnlZgM3drHlei8X77nRx4Bzq63vM2g94FKmZLERUlT5Uwzir/BPJzj8lbjxiKVcXtnDNPm165E7VSS6t9sF65eXH74jYSSldO8Y6/hd1t/Q0LEotLmFdyVwLgPU6Vm6+AgpivI12PWqnHQ23N7DpHxdeoI0cQmtnD+7T5PHz5eZo5xrpapIdBU93fTL2y7J+LTBrb3svnb34nUqOPMLkFBI6aFxx0seFyHF4ehk6NEWdxFoM958n8xkcWMSg8yO6CLuGEZmTwqzQUNnCaki0SnGrbxqEjWKUfIrLQHYP9/6Po0GGOb5ECKGSnkV/eOvAM14Om/IvKUNr7J5fRzTHksbRxF9t+eGfrlvkyoSRlJ6lOjkIuUha3ECDRDSuejP2zuHne605qXvSxEYISXgm3eE8PQuf8HwhChx4xGDzI7oLjwwfG5U9y0rYSSlR4lOLvLnzlVtDpQpX7TnxJ4Fzv9hfZ+eX7Dq6oSIKX+ovaVKIVe3iBSIiNy82H1WirRxlICjjHvRAZTo5KO4py05Dtgzq/D9Wo8qeUyElJRPdXZvqdnvvWPixSKW/C+UWWnSxqFClOjkgOOA6CNsuUaXoj3n1l72HEcXy/sMWEUVUIg08o/o0h+zD/56fSUNRxSunuw+Jx3Q6aSNRWVUmeiSM2RWa+7pHfaB4OgKVG1R+P46reFoTmtlgnz9fraJj5DicvMC3LzZctJ9oDbP1JZM+Z3is8qlwCWCbDqqE5NqEt3Soc31yxvPPpAwkhK4lzf0v2rzorXNubieTSdw9bK8z/BtJSsITYiteFRi9+kJQPW25o+nxIobj9CcXFlBawDISpU2lkIoaQ4doKJE16NBJf3y51tl1uX3fgS7z68RaE1OpmE6gbXRlkHtSx8XIaVRpgK7T39iOJVZULLMvpAWRqMBnPNGL+Y8lzaWQmyKNHzJ+KRnXQkjsQ3VJDqNnI9e7p9g90VJdKkPAXdvwLOq5X3e/NcmYRFSKmV92f3zRP6zC0pLdIDhmridd2iYvvmSfnlwaKCEkdiGahKdbKXGA09vA9AA1YrQZLV8CGuzU6Or5X3ym18SIqWCR3R8Em+JF4tY8hMdZ9+JriAvd2epQyg1SnT2LvYsu/eryz+xlo+Do+UCzoPW07U5Yh/KFDii45M/0lhJNHkfuXZ+RKc0qk10srnYmt+bK7+1SVFc32n5sdo9ShcPIbbikn+9ykJHESWWAdPI74hOCVSV6D7uWUe//O+FhxJGUgz5/9krNy76c/4cyL/9lWV0NEfsh7M7u8/NS3T5JbKUTH/q0n7n0WVkKy8JqyrRjetUQ7/88d8y6WL8KC/Oonb9fmqlDVHD10sfDyG24pTXVSQnk91XqC1dLGLRJzj7/cK5aP9N/fKcvg0kjMR2VJXoZDfyMv0JkJI38iy/WWVhFlk4xdlmAmuPQoi9MD2iU0MHjdy8pO7kZn0/CS05eFu/PKi1/EdcAipLdLKTf9qyfA3A1aPw/a1d4O74oW1iIsRW8svT5eZV73EvYrFyOcv/WYtS+MEOuDgpI0Uo46cooVyt/Z4nBwAkXGP3+b27CrNnJv/2gNZFH7FJiGg4dpc/ElENf6PaLHZvrQYtsTnVJboxnUL0yxvsvRRYYt658qJeuzjxA//2fha2EyKl/OtV+ZcU+BIdx4kXj9A4zlB71k5PXaZmyqwOcBGpLtFNLVDOZtqmS1b2tANP8ibM+hahjX38FcuP+dWx/BghUuFMj+i8zffRKuiDN//6HAA42ecR3ft/ntMvfzOgiAPgZEB1iU5WA1L0R3Q1C993CU9RXADo/bXt4iHElvRHdHkfQ07u5vsUTA5yp+/GoAFcinDNXQIHrj/WL7/SzEoZQZlRXaKTjcxkIC2eLRd2RGft9E7TwbaLiRBb0o9AtDIww47nmxVbZhK7d/MCHOz/o9dB5l3FC7L/37bA7j5JlzoEfvmnLctVBNw8re97aQP/9spNDdUnCLE3+a1q8kcU63hOUzrKv86iXkYSu+c7RWsHdDoFXQ81ocpEd+6zF/XLXb4+KF0g1iRFs/vyIVZ3AwBsGsW/vc+3NguHEJszTXR81+McFDT3U39E5y1lFBb9fNRQbOLF+sqqUqPKROdT1j4vBBtJzusHZa3dDgBocy0/VrW55ccIkZrZER3P37KiEl1ef0g7PaJbsD1Kv7x4UDFq68qAKhOdLOR3V/YqJNFF/MS/vdEAqmtJ7FtW3uCM/ETHN/BEo6CPqPS8gR75XRvsmJuzo9Qh2JSC/opK7kJMktQhmMtvOukZYH2/PZ/xb+/4kW3jIcTW8o9wXPOuQfO161HSl7WUvELyHpWljYNHjr0Xzygl1Sa6y3MM7Wr6/XhMwkgsKMoRnbXRljR3jti7tAR2X9aP3afIpKNISaU+Yvd2mOgmrTuvX36/axGmM8mMahNdOVc7P/ef/5/e2jW6C3/yb2/5tu3jIcTWTD/487/cKVVK3s/raX+JbtulR/rlSWHK6yKh2kRnyq4O3TmOdS4AgHL+lvfbMo5/e+hY28dEiC1xHJAax5Y9KrF71RzRVZE2jkIoaf5cPlUnuk8KlAMbs/qshJGYyEw2dCAuSUV3NfT1IvKWmWQYfJKf6JJiJAtHcDqdIdHZ2RHdufvPpA5BcKpOdOM6Gxqx7o9KkDASExl5f3jOZQBnC8VfH57j3x7UQVkX8Iky5R/NuXkb+tKl29H/QVtLfcgSu4NT4QPMRPbKT8f1y0c+7iJhJMJRdaIzxdlLpfSMp+ze2tHcP+/xb+/0se3jIcTWku6zey8rH/o1uokTixgS85qZ+gTZdQPkauXLSB2CIFSf6AoOSll/2k5OnTzPO6IrY6U/V7yFzguBbWwfDyG2lpjfmaOG5X2U9Lf8NK/qSFEqHYnoaXq21CGIQvWJ7uKs7vrlqfbStqewUkGWOolrHJVVG5AoV/4RTnkric7TvgdtFMvTIvy8Emg+d49++Ze3WkoYibBUn+jscoRRznN2b6kgs6Uizl0/FSYeQmxNf0SXN2eL77KBh4LqLSbmHdFZO4KVWLd6Cvp9m1B9ojO18/KjwncSWk5++xILA1G2vMu/vV4/YeIhxNbyT+XlJ7r0x+b72OHE6hLL7y1pR6cu1XLaEqBEBwC4Ma+XfnnsH5ESRpIn/4jOmacRJWCYemDKjr8tEqKXlQok510Pz090dw+b7+ddXbyYhJSTYTiCrdhA2lgKKHjacskQZReAp0QHwMXJ+Ncg+ejLXCtHdJZiK1eRphUQeYi/wu49qgBl8woc395vvp9rOfFiElLCVdZAtkwF9v/UDvVqpKCjZx6U6PKUcTFU6/5m9w0JIwH7BgjwH9HdPcT/nPaThYuHEFt6dJHdV2pk2HZzD/++ShB3md1XamQ3X0ZvP06TOgRRUaLLc6VAkecfDtySMBIY+nLx9eI69BX/c2p0FS4eQmwpLi/RVW5s2GY6WdwnSLRwBBeXN5q7UkNp4yig2zeGL8yb320rYSTioESXR2PyTcs+al/ynKa8d5R/V1/lVRwnChXHc0Rnqvlb4sQihvi8I7qKVn5eCTULtDJfVyEES3TR0dEYOXIkgoOD4e7ujho1amDWrFnIzrbfkT4FS4LV+nSHdIHkJ93iXCt0oO8sRAZyMoD4q2y5chN2r+P5UlmhlngxCUmnLXBEZx+Jbtmh21KHIDrBatFERUVBp9Nh2bJlqFmzJi5fvoxRo0YhPT0dX3/9tVBvWyqf9KyLJQft4Y/Awnl8bQ7/9np9hQuFEFt6eB7Q5QBl/Q2jKh/yjHSuaD+n+Uol4SqQncaay9pJj8jwHVH65YKXbJRMsETXs2dP9OzZU78eEhKC69evY8mSJXab6ExdepCMRgFeUodhcGsv//Ymb4gbByElFRPB7gNDDWcuLq43308p1+hiTrL7qi0AB0fr+4ogPSvXaL2svffltBFRz3clJyejfHnLhYqzsrKQkpJidBPbqU8NhWRf/sHC9TChafL+WTiTUzpnV/HvX6WZsPEQYiv38z74q71g2Mb3d20noxNLLeYUu68WKm0ceRrM2qVfntBFPdf1RUt0t27dwuLFizFmzBiL+4SHh8PLy0t/q1atmljh6fl7GM9d0+okmFOXP60gf5pBvhsWrhsqqYIEUS6OMxzhBBZIdNos4/1qKeh0Wv7PW621tHHw+LCHfZxKFUOxE93UqVOh0Wis3qKiooyeExsbi549e2LAgAEYNWqUxdeeNm0akpOT9beYGGm6CfRtYigmW2P6dvEDsJToLFHKt1+ibPFXWAsq5zJApbypBXwDruorpJRdWgLwLBqABgiQvmDyN7uvSx2CZIp9gnbKlCkYPny41X1CQgz13B4+fIguXbqgbdu2WL58udXnubq6wtXVtbgh2dyiQc3w74WH0gXgnNcTKie98H396ha+DyH24PY+dh/UAXByYcuPzpvvV6WpWBEJK/oIu6/YAHCT/lr/4v2G+cFqGYSSr9iJzs/PD35+fkXaNzY2Fl26dEGLFi3w22+/wUGmQ+BXHL6DUR1FLMaqT3QFjui0ufz71u8veDiE2ER+ma+CxQ0ilpjv51dPnHiEducguw/pLGUUAIC7T4y/NKtlEEo+wTJPbGwsOnfujMDAQHz99dd4/Pgx4uLiEBcXJ9Rb2lTBQs/zt18T981d8hJd9nPDttgz/PtWV35VA6IA2c+BeyfYcsFExzfiUqZfiI1wHHD7IFu2g0TX5euD+uU179jHwBgxCZbW9+zZg1u3buHWrVsICAgwekzyoslFYFro+fbjNNTwE6nIrKsnu89MNmyzNLVAKcOwibLdP84GnXgGWJ8M3vEj8WIS0rO7QPJ9wMFZ8i+jaSZTCtrVrCBRJNIR7KvT8OHDwXEc700u9nzQUb9csDac4Mrm/SE+TzRsu7GLf1/PqsLHQ0hp3cq7Pleji2HwVBpPD7qQLuLFJKT805bVQi03UBZJwwJTCga2FH8kuz1QwDkC4dSq6GG0npppoTKJrZXJa13yPNEwKi2/PqApR3WdaycyxHHAta1suVZ3w/Yj35jvW1UhfdHyr0dKfNrSdHrUF683trCnslGiK0T4q4b6dI1m7xbnTd3zJtXrcliTSkLkLO4iO43n5A7UDDNsP8kzEMVSs2E5yckEbuUluprdrO8rsILTozzd1PulmBJdIQa1DjRaz8q10N3bllzKGEZePn9ieT83b+FjIaS0rv3H7muFGQZa8ek8XZx4hBZ9hE0N8qgiadUi08tEF2Z1t7Cn8lGiK4LRBaYW1JmxU5w3zb9Ol5ZgeZ/K6jwNQWQmP9EVLD7+iOdUfJ2e5tvkKGobu6/TS9JiDiEmxS5MW5GpCSW6Ipje23heT3auCL3qvPIuGic/sLxPJUp0xM49uQk8jmKjDwten9vxifm+dtqvrVh0OuB6Xqm+Or0lC4MN/DOs314gXSz2gBJdEb3a3DC6sfYMEXrV6RNdjOW+dBUbCB8HIaVxaQO7D+kMuHsbtt8/bryfe3llzJ97eA5IiwNcPIDgDpKFETzN+GjO0UG9R3MAJboi+/Z/TY3WM7IFvlbnlTf3MCnGeD4d3z6E2COOAy6sY8sFW0llPDPft488WncV6uoWdl+zG+AkTTlDnclIS7UfzQGU6IpleNsg/XK9mQJfq/MucOoyxULdzbJFK8VGiCTuRwBJ99jRTcHTePvmmu9b80Xx4hKKTgdc3sSWG74qWRim1+bUfjQHUKIrltl9jU8VJqZlWdjTBvKP1pJjLCc6Vw/+7YTYg4t5R3P1+xqPtjzzi/m+bp7ixCSkmJNAygOW2GtJM8LR9EzTHTqaA0CJrtgWFphX12KehbJctuATzO6f3mHJjo/EFRcIsSgnE7iymS03Hmi83dRL34sSkuAu/83u670s2XzAgmeaKpRzgQMdzQGgRFdsb5jMqzsd/VSYN/IJAhxdgdxM/lYmAOBMiY7Yqav/sGvLngGsLU++fZ+b71u3j3hxCUWbC1zZwpYbvSZJCAmpxl8iTn8aZmFP9aFEVwKb3zUUaR2w9IQwb+LgCPjmtbp/cJZ/n/yeXoTYmzO/svsWw41HU0b8aL5vOX9RQhLUnQOsuEOZCkBwZ0lCaD1/n355eNsgVc+bM0WJrgSaBfoYrX/89wVh3sgvr9V9/CVhXp8QIcRfAWIiAI0j0HyYYXt6ovm+/X4SLy4hRf7O7hu9Lkn92V1XjNufmY4nUDtKdCV09XNDh96/zjwQpitDfqIjRE7yj+bq9gE8Khm2/zPefN96L4sTk5DSHgPX80Y6Nn9TkhDGrDac9Vmrwn5zhaFEV0JlXIy/tZlO0LQJSnREbrJSgQt5zVRbjTR+7AZPoQUljLa8sBbQ5QJVW0pSxKFgU1UAaKvCfnOFoURXCtELjS+iP0vPtu0bUIkvIjeRvwPZqYBvLSDI0M8Rj3hO7w/+S7y4hMJxhtOWBU/TiiQzR4u7T9L16xdnq7dwszWU6ErprTbV9cvN5u6x7YuXDwFcvWz7moQIRZsDROS13mk7wXgQyrKO5vvX6CpOXEK6dxxIvMVGQDcUf7Rl3c+MC1d4ujmLHoMcUKIrpTn9Ghqtf/7fVdu9uEYDVGlqu9cjREhX/2FzPsv6AY0LlPzS8jQsbjIIcFTAh/KpZey+4auiF3AwHYBieoaJGFCis4FTnxqaK/567K5tB6YopeMyUTaOA44vYsutRwPObobHds8w37/zVHHiElJSjKFz+gvjRH1rjuOMBqD8OJg+J6yhRGcD/h5uRus2HZgiYeNGQoos+gi7DufkDrQ0GYRycqn5/j5BooQlqNMrAE4LBHcUfRCK6WdMn8aVRX1/uaFEZyOmpw32XYu3zQtXbWn5MW2ubd6DkNI6/BW7bzYEKOtr2H4/wnzfN9aKE5OQstOBsyvZcqi4R3O3ElKN1q/PU0jDWgFRorOhX4cbktLIVWdscwrTq6rlx3LSLT9GiFiijwF3D7Pmqu0mGT/2aw/z/WvxbJObC+tYiTOfIKC2uD9P2LeH9cuvNQ+Aq5OjqO8vR5TobKhr3YpG6zY7hdnAQsuP7Oe2eX1CSuNgOLtvPszQXgrg77rR8SNJKofYlE5rGF0aOpaV6xNJ0NRtRuvf/K+JaO8tZ5TobOxuuHFbDNORUSVSy0Kvrsyk0r82IaVx9wi7PufoAnSYYvzY9zzzQNtMECcuIV37F0i8Cbh5A02HiPa2Vx4aN2C+MkcBR8YioURnYxqNBkuHGkZAjVl9tvSnMKu349+e+qh0r0tIaR1cyO6bv2nc8T4nE9CZTCuo3g5w9xYtNEFwHHD4G7YcOla0yi4cx6HPoqP69V4NK6Gsq8yPjEVEiU4APRsaj4Aq9SlMn+r82x/fKN3rElIat/YC946yo7n2k40f+72f+f79l4gTl5Bu7GJF1l3KAaFjRHtb08+QJUNbiPbeSkCJTiCmpzBn/XPZ9m+SYMPJ6YQUh04L7P6MLbcebTxoSpvDuheYsvSFTS44zjC6tNVIoEx5Ud72n/OxRutRc2mUZXFRohOIRqPB1vfa69dXnbiH1EyeChGl8TDStq9HSFGdX8O+aLl5Ax0/NH7sz0Hm+489JkpYgrp7CIg9Azi5iXatMSNbi4nrzuvXZ/SpBzdnGmVZXJToBNSwqnGdykazd9v2DeKoTx2RQHY6sH8+W+70CeBeoD+jNhe4xVPztVJD821ywnHAvrlsuflbojWLrTfTuJblOx1CRHlfpaFEJzDTieSmw4OLrOHrNoiGEBs4/gOQFsfmkLV6x/ixdXxHc0fNt8lN1DZ2NOdcxnx0qUBCphl/VpheDiFFR4lOBDfm9TJa//nIneK/SJ1ehe9DiNCe3QOOfseWu80CnFwMj+VmAzd5zlpUaiRObELRaYF9n7PlF94FPCpa398G9kfFQ1dgsPbBDztDo9EI/r5KRYlOBC5ODvhuoGFi57xt15D8vJjX6yy1NKFJ40RMu6YDuRlAUAegwSvGj/3Y2nz/MUfEiUtIF9YBT66zU7Tt3hf87Z5n5+LtlWf06y81roygCmUFf18lo0QnkleaBRitN/m8mNfrLI3wenq7hBERUkw3dgNRWwEHJ6D3V6yNVL7nT4Fnd433d3AGKsu8eXBOpqHyS/vJgJvw/SHrz9xltP4DdSYoNUp0IrLZ9bqCru8sfB9CSisnE9jxEVt+YRzgX8/48S+DzZ/z3hnzbXJzcinrsedRBWg9SvC3M/1MoOtytkGJTmR3Fhj/4baav7d0L3hpQ+meT0hRHPkGeBbNPvA7fWL8WCLPWYXq7eXfiic1zjBvrttngLO7oG83ZrXxF4PIz16k63I2QolOZA4OGuyb0km//jg1CxvOxBTtyTW6mW97ct1GkRFiQdwl4Oi3bLnnAvNO2ot5Tq0NXC18XELbOwfITgOqtjDumC6A47eeYNcVQ2uvrwc0QfmyLlaeQYqDEp0EaviVw1ttDFUiPvr7IuKSMwt/YruJAkZFCA9tDrDlXUCXC9R7Gajf3/jxc3+YP6fDFNGqhgjmwRngQl7fvF5fAg7CfVQmPc/G4J9P6tf9PVzxeosAK88gxUWJTiJz+hlPoH0hfB+0ukKKPwd14N+eaqMmr4SYOr4IiLvIKqD0/sZ4AIpOC/wz3vw5pqc25UanA3Z8zJabDAYCrDQ/LqVcrQ5NPzeeYH/q0zDB3k+tKNFJyHRwSo3phRR/tvSt8vJGG0VESAGPrxu6E/T6wnz+2LJO5s8ZshFwchU+NiGd/wOIPcsKN4fNEvStan66w2jd9DOB2AYlOomZjqoq0UjMI9/YKBpC8mhzgC3jAG02UKs70Hig8eMpD1kVf1O1ZH40kpYA7J7BljtPBTwqCfZWpv/Xb86nohBCoUQnMY1Gg+vzjKuRW012XT8z3/b8iY2jIqp3cCE7qnHzAl763viUJQB8W8/8OZMUUHt151QgMxmo3AQIHSfY25j+Hz/6SRc4O9LHsVDoN2sHXJ0ccWyqceWTWp9aOI0ZOpZ/e3a6jaMiqhV9zHCW4OX/M27BAwD755k/p/UYwDtQ+NiEdHMPuwygcQBeXgQ4CtPYdNgvJ43WfxveCgE+ZQR5L8JQorMTVb3d8fvbhhJKOVoO76w6bb6jazn+F9g1XaDIiKpkPAM2jQbAAU2Hmpf5ykw2zC0rqDtP8pOT7HRga17z2BfeBao0FeRtvt51HUduGs7AvN+1JrrUFacTgppRorMjHWv74aMedfTre68l4Ls9RewifnalMEER9eA4YOsHQMoDoHwIG4BiaiHPUduo/cbFneVo7xwg+T7gFQh0EeZL47pT9/HDgVv69ZbVfTC5ex0rzyC2QonOzozvUhOdavvp1/9v302sO3XfeKeBPHOXAHYhnZCSOv0zcGUzq2X52s/mZw+O/2D+nOBObEK1nN0+AJxaxpZf/h5wsX0B5b1X4zF1k/E1zL/HtbX5+xB+lOjs0Kq3W8PD1XB9YOqmS9h+6ZFhhzoWhiDT6UtSUg/OADunseVus8yTV8YzYPen5s8bvF742ISUkWSYC9jqHaAmT/WhUjoT/RTv/G5c3oumEYiLEp2dujSnh9H6u2sisT8qb2K4pfl0lzYAWakCR0YUJ/0J8NebgC4HqNcXaPue+T5fBJlvG7FD8PqPgtvxCZASy07Vvvi5zV/+QkwSXl96wmgbJTnxUaKzY6b/Id5eeQaHbjxmK11m8D/p9M8CR0UURacFNo5kH/a+tYB+P5pPJdgw3Px5dfoA1WV+6u3qP8DFdWyU5SvLbH7K8uy9p+j34zGjbZTkpEGJzs6Z/sd469dT2H0lDmj/Af8T9s6mqQak6PbNAe4cBJzLsELMbp7Gj8dfZdftTA1YKUZ0wkm6D/ybd+Ta/gOgGk/T2FI4fvsJXltCR3L2ghKdDJj+Bxm9+iz+inxkYW8AZ34VOCKiCOfXAsf+jy33XWzeY06bCyxpY/68CWflPcpSmwP8PZJNlajaAug01aYvfyAqAYNXGM+VoyQnLUp0MmH6H+XjjRexq85c/p2PLQKyn4sQFZGteyeAf99nyx0/Ahq9br7PXF/zbT3CgQo1hY1NaPvnAQ9OAa5ewOu/2jRpbzz7ACNWGs9/pSQnPUp0MmL6H2bMhRD+HdMTgMhVIkREZOlZNLB+CBt8Ur8f0JlntO4/E/if+4JwZbFEcXMPcOx7ttxvsU2bw36xMwpTNlww2kZJzj5QopOZ6IV94O7smLdmpfvw0e+BnCL0uCPqkvEMWDsQeJ4IVG4K9F9qPor3fgRwjqdx6rRY84EqcpL8ANg8hi23GsWSvI0MWHocSw4ad1qnJGc/REl0WVlZaNq0KTQaDc6fPy/GWyratbk90TzQGwDQPut7/p3S4oDI30WLichATgaw9g3gcRTgURkY9CfgYlJjMTsd+LWH+XPfPWm5/Jwc5GQA64awBF+psU1LlgVN3YbT0c+MtlGSsy+iJLqPP/4YVapUEeOtVGPTu+0wpmMIHnBW6uQd/Q7IzRIvKGK/tLnAhhFATATrSDB0E+Bp8n+S44AFPP9P+/0E+NcVJ04h5Jc2e3QecC/PKgs5u9nkpU27EDQP9KYkZ4cET3Q7duzA7t278fXXXwv9VqozrXc9LBvWAlOyLXQ0SH0InLNQLoyoB8cBWycCN3YATm7AoHVAxfrm+83xNt9WqTHQbIjgIQrq5DLgwp+AxhEY8BvgU73UL5mj1Zklufe61sSmd9uV+rWJ7Qma6OLj4zFq1CisXr0aZcoU3oYiKysLKSkpRjdiXY8GlfD+lJmWdzj6HZCbLV5AxP7sm8O+8Ggc2ChDvoneaweabwNYwWY5u3vYUBqv+1wgpHOpXzIhNRO1TDqDrxzRClOoQLPdEizRcRyH4cOHY+zYsWjZsmWRnhMeHg4vLy/9rVq1akKFpyjVfcsit5GFD6rkGODy3+IGROzHwS/Ylx2ANVCty3Na7fQvwI2d5ts/iQYcnYWMTlhPbgLrhwGcFmj0P9Z+p5SO3HyM1vP3GW07NrUrOtehVjv2rNiJburUqdBoNFZvUVFRWLx4MVJTUzFt2rQiv/a0adOQnJysv8XExBQ3PNVyemWp5QePfg/odKLFQuzE4a+AgwvYcvd5QIu3zPe5HwFsm2y+/b1IwN1H2PiElP4EWPM6kJkEVG3JGsiWcsTo+LWRGPbLKaNt1+f1RFVvmdf7VAENx3FccZ7w+PFjJCYmWt0nJCQE//vf//Dff/9BU+CPS6vVwtHREUOGDMGqVYXP80pJSYGXlxeSk5Ph6elZ6P6q91sf4N5R/seGbhKkMjuxU0e+ZacsASBsDtB+kvk+z+4B/9fYfPub/wIhnQQNT1A5GcCql4EHpwHv6sA7+4ByfoU/zwKO4xA8bbvZ9rvhvY0+34iwSpMPip3oiur+/ftG19gePnyIHj164O+//0ZoaCgCAgIKfQ1KdMWk0wGf838L35DbES/N3AJ3F0fex4mCHPs/YE/edduunwEdPzTfJyMJ+IJnUEbvr4HWowQNT1A6HfD3cFaw2c0LGLkX8Ktd4pdLzshBkzm7jbb5ebji9KdhpQyUFFdp8oFT4buUTGCgcSficuXYHJwaNWoUKcmREnBwABq8ClzZZPZQd8czaDRzK755oyX6Na0qQXBEcBwHHAwHDuV1Bu88nT/J5WbzJ7mWb8s7yXEcsHMqS3IOzsAba0uV5PZejTfrI/fV640xoCWNHZAbwRIdkcjrv/ImOi/Nc7R2iMLEdU6YuO48zfVRGp0O2DUNOJl3rbbrDFbD0mw/LTCP5zRepUZAn2+FjVFoB8MNncL7/wQEtS/xS9X7bCcycrRG205/GgY/D9fSREgkIloJsKCgIHAch6ZNm4r1luqk0QAvfcf70NuOhiHRQVO3ITuXBqgogjaXdcnOT3K9v7ac5D4vz/8aow/Lu7zXiZ8MR7K9vwYa/69EL5OWlYugqdvMktzd8N6U5GSMal0qUcu3eTeHOZ5DZRgGEtWesQOrjkeLFBQRRPZzYMNbwIW1bEL0K8v4Tz/qdJaT3GdPLHetl4Nzf7CjWYA1JC7h6de/Tseg4axdRtv6NKqM6IV9aNCJzAk2GMUWaDBKKTy+AfzYymyz1rc2asTONttOI8hkKC0B+PMNIPYs4OjKqn7wzZOzMkgJMxIAJxkfqVzZDPz9NsDpgDYT2DSKYv4dWxpVeeDDzgiuYNuu46TkSpMPZPw1jlhl4SK8Y+INRE+uYbY9eNp2XHtElWhk4/F14OduLMm5+wBv/sOf5LS5lpPcp/HyTnKXN7IGqpwOaDa0REnuelyqxakDlOSUg47olMzaN/nZydh9JQ6jV581e4gGqti5u0dYP7nMZMAnGBi6EfA1//KCnExgfkX+1/g0DnCW8UTnixuAzaNZkmsyGOj3A+BQ9Kkzlo7iPu5ZB+92lnljWYWiIzrCz8EBGLyB/7FtU9C9QSXcXtDb7KGgqdtwPS5V4OBIsXEcK1C8uj9LctVCgXf28ie5508tJ7npj+Sd5C6sNyS5pkOLneSi4lJ4k1zU3J6U5BSKjujUYLYX//YPrgBebE7jwh1RWHrottkudHRnJ3IygP8mARfXsfVGA4C+P/C3m0m8DSxuzv86Mx4DTi6ChSm4c2vYCFNwQPM3gZf+r8gDaSwdxXWq7YdVb7e2caDE1uyyMootUKKzEWunMGcl6a9r5Gh1ZlXZAWDp0Bbo2bCSgAESq57dA9YPBeIuspGV3eeyAsV816Nu7ALW8gytd3RhpyuLceRjd44tAvZ8xpZbvg30/qbISY5v8jcAnPvsRfiUlXHiVxFKdKRwCVHAT6Hm2x2cgJnGtUu/3XMDi/bdNNv1+ryecHWS8QelHN3YDWweA2Q8Bcr4AgNWAsEd+ffdOwc4yjPpu1oo8PYu+c6T4zhW0uz4Irb+wng28KQISS4tK9dsygAA9GpYCUuGtrB1pERAlOhI0Wz7EDi9wnx75+lA50+MNml1HGpMNz/NE1i+DA5/3EWoCEm+3Cxg72wg4ie2Xrkp64ztbaH81OIWQOIt8+3tJwNhs4SKUnjaXODf99g8QYAVqG43sUhJu98PR3HhQbLZ9qi5PeHmTF/Y5IYSHSk6S9fr3tkHBJj3DTxxOxGDVkSYbV/xZku8WN/CYAdSOk9uAn+PAOIusfXQsewDnu96nLXT0gP/AOq9LFycQstOZ3Pkbuxkp2z7LmLTCAqx71o8Rq4yP0258NVGeKN1IM8ziBxQoiNFx3HAHG/+xz66DZStwPtQo1m7kJqVa7b9zIwwVCgn47lY9oTjgMjfgZ3TgJx0wL08q9lYpxf//kkxwPcN+R8bfQio0lSwUAWXHMsmw8ddBJzc2ClbS7+HPLFJGWi3kL8jOhVEkD9KdKR4slKBcAsdJKY9AFw9eB/KzNGi7mc8nagB3JrfC06ONFulxJJigP/eB27nfVAHdQBeXQF4Vubf/9QKYDtPZwLAaDStLMWeBf4cDKTFAWUqsC4EgTzXl/NY+7s8P/NFeJehwSZKQImOFN+TW8APFi7GFzKZ+OKDJPT94RjvY/TNuZg4Dji7Etj9GZCdykp5dZ0BtBlveYRkeDUgy0IVG7lPBL+yGdg8FsjNBPzrA4PWAT48LYVg+ToyAPw0pDl6N7LwJYHIEiU6UjK39gJ/vMb/2Kfx/NeECvhyZxR+Omg+987d2RFXP+9BCa8wibeBrR8Adw+x9WqhQL8fgQq1+PdPjQe+sdBfre37wIufy3dkpU7Hug8cWsjWa3UHXvsFcDP/f6/TcWg5fy+epmebPUajKZWLEh0puTO/sg9bPlNjeD9oTLUJ34dHyZlm26t6u+PY1K6ljVB5sp8DR75hw+W12YCTO9BtJhA6xvJRnKWpAwCbOhD4gnDxCu35U2DTKPbFCwBCxwE95pv9LjiOQ7dvDuHOk3Tel6GzCcpGiY6UTsGJuKasDFApyFLViXz0IQR2mjJqGxtsknyfbavRDej9FX8ZL4BNM5jnb/k1P7wFlONppCoXD88B699kvw8nN+Cl74Gmg4x2ydXq0GTObqRna3lf4vaC3nB0UPnflgpQoiOld+RbYN8c/sfejQD86xXpZaxdNwGAm/N7wVmNg1YeXQD2zALuHGDrXtWAnuFA3Zcsn248uRzYwdNAFWBHPT3D5XuqkuOAyFXA9o/YUa1PMDBwNet0nic9KxcNeCZ756MCBupCiY7YhrXTmK/9AjR6vcgvVVjCOzsjDL5qmJbw7B6wfx5w6S+27uAMtHsf6DAFcLHQBsbaqFgAGHsMqGRhWoEcZDxjdTuvbmHrdXoD/ZcA7t4AgIdJGWhrYZoAANyY1wsuTir8sqRylOiI7dzaB/zxKv9jDV4FXvvZJu1Q8n0/sCn6N6ta3CjtX2ocOyV8egU7YgFYIeauMwCfIMvP2/IucH4N/2MV6gBjDsl7VGX0UWDTGCDlASs/13UG0HYi4OCADWdi8NHfFy0+laawqBslOmJbFrqT631wFfAqXnLiOA5v/noKR24+4X3c0UGDG/N6yf9aS3IscOx74OwqQJvFtgV3Al6cA1RpZvl5908Cv3a3/LiFyjWyoc0BDoazU+TggPIhwGs/I6tiUzSdswcZOfzX30L8ymLf5E50fZdQoiMCyEoDwq0ks/5LgCaDSnSNaNvFRxi/NtLi42veCUW7moUPgLEribeB44vZ0Vj+EVxAa1ZDtEY3y7+nzBRgoYX6lfmvMXyrvDuBJ0QBW8aygScA0GwoDtf4EG/+cdXiU6b3rovRHS0M0CGqRImOCMNauTAAcPcBRu1n385LIDEtCy3m7bW6z9XPe6CMi1OJXl9wHMcGl0QsBW4WGDRRvT3Q6SN2JGcpwem0wFc1WVcCS949CfjXtW3MUjjzG7B1EnRu3hif8hZ26CxXOdk/pRNC/MqJGByRC0p0RFg7pwMRP1p+vN0koMNkwM1CwehCcByHEStP4+D1xxb3qV/ZE/9OaGcf12gyngGX/gZO/wI8vmbYXqsHG2gS1N7yczkOWPUyEH3E8j59FwPNhsl3RGUBmTlaDF0RgXaxv+BPbVckwLwAdS3/ctj9QUc6PUmsokRHhJd0H/i+kfV9eiwAWowAXMqU+G0eJWegTbjlEXcAEFavIpYPawEHMa/n6XRA9GEgcjVw7T/D9TfnskCzIUDrMUCFmpafz3HA6lcM0wv4VG0JvPkP4CrvI5qsXC3G/RGJ/VEJVvfb9n57NKhSsi9HRH0o0RHxWGrzU1DnaUCrUUBZ31K91eoT0fjsnytW9/Et64LDH3dBWVcBTm/qdEDsGeDKFuDqP2ykYD7/+uyoq+lg/bB4XrnZbGDPs2jr7zU5ynIBZxl4lp6NV346hujE51b3e79rTUzuXkekqIiSUKIj4oq7BCy1cnouX+OBQNMhrBJ/EbpBW8JxHN5fdx7/XXhY6L5b32uPhlVLcZSQmwXcPwFc3wlc+xdIiTU85urJ5hI2G8ZGUFo71ZbyEPi2CJPsx58G/CzUr7RzZ6Kf4vWlJwrdr2k1b2wc11b+I2qJpCjREWmsfsXQVsYar0Cgfl+gbh9WuLgY8/BMaXUcxv5xFnuuxhe6b/myLtjzQUfrE9M5DnhyA7h9ALi9j83zyilwVOLiAdTpCdTvD9TsZn0OG8cBZ34Btk0p/AeR4aTvmKfPMWDpCcSlmNc1NdUkwAsbx7W1j2uqRBEo0RHp5GQA8ysVfX/38kCNLkBgG6B6W8CvXomP9jiOwy9H72LetmuF7wzAy90Z29+pj6qZN4EHp4GYU+w+M8l4x3IVgRpdgXp92X0hXRzw9A6wyMocuYImnLHcncDO3HmchqE/n8RDnoLdfEa2D8aMPvVoUAkRBCU6Ir3kB8B3DYr/PFdPVkfTvz5QsQErbuwZwCakWyqRZUHM0+fo8OV+eOI5qmgSUVmTiKqaJ6iheYjamgeo7fAAfppks+dxTm7QBL7AklqNbiyOwj6s0x4DK7oaijNb41cXGLbFrq/BPc/OxeoT9xC+I6pYz9s5qQPqVqL/m0R4lOiI/Ui8DSxubpvXcvNmnRNcPQCXciwpOrkAnI6dJgTHKm5kJrOJ11kprOVLDn8bl3z3dX44x9VCpI7drnGByIVhMEtYPX989lJ9VPc1SbSxkcCKLkWP/8W5QOvRhR8RiojjOFyPT8UXO6JwwMp0Dkvm9G2AN9tUp6M2IjpKdMT+pD0GvrYy3J5PQGuWrJJjWbft0nAvD3gFsFv5EHB+dXExuwoGb3mGdBStVmQlJGKh88/o7HiheO9djG4PQuA4DvcSn2P31Tgs2F68IzRTiwc1w0uNK1NiI5KjREfsl04H/PMucOHP4j2vfn/WZdqnOpCdzir6Z6WyI7j8D12NhnUDcPNiDWJdvdhQf4/KRZrLl5mjxRc7o/DbsWh4Ig39HY/hc+dVxf4RAWBk9hQc1DWFFo4I8HHHq80D0CrIB1W83VGhrCs83JxKPO+P4zikZ2vx4Nlz3Et8jsuxydh68RHuWmhAWlKvNQ/A3P4N7LcSDVE1SnREHooy6bww9fuxgSxVmgN+dViSK+xog+PY6c2nd1i9xaitRRstWojh2R/hmK4RciC/xLBoUDP0aVSZhvwT2aBER+THltfyRJIb0g3b/Edh0sFccLD/YfMfdq+NIaHV4VPWRepQCCk1SnRE3nKz87pNfyh1JMbq9Abavg9UbV7k7gE5Wh3ikjNx8u5TnLqbiOO3E/HgWYZNwqnk6YYXQsrjhRBftAoujwAfd+qwTVSDEh1RFp0OeHIdiPgJiPxdnPds/ibQ6H9smkMpS5cRQmyPEh1Rj6w0VpYr4Sq73hZ/FXhwil2D4+NZFajeDqjcBKhQm83P86jMWgzRSEJCZKM0+UB+V9GJurmWY4NQ/OoADV6ROhpCiAzY/xV1QgghpBQo0RFCCFE0SnSEEEIUjRIdIYQQRaNERwghRNEo0RFCCFE0SnSEEEIUjRIdIYQQRaNERwghRNEo0RFCCFE0SnSEEEIUjRIdIYQQRaNERwghRNEo0RFCCFE0SnSEEEIUTdBEt23bNoSGhsLd3R0+Pj7o37+/kG9HCCGEmBGs8erGjRsxatQoLFiwAF27dkVubi4uX74s1NsRQgghvARJdLm5uZg4cSK++uorjBw5Ur+9fv36QrwdIYQQYpEgiS4yMhKxsbFwcHBAs2bNEBcXh6ZNm+Krr75Cw4YNLT4vKysLWVlZ+vXk5GQAQEpKihBhEkIIkYn8PMBxXPGfzAngzz//5ABwgYGB3N9//82dOXOGGzRoEOfr68slJiZafN6sWbM4AHSjG93oRje68d5u375d7Jyk4biip8epU6fiiy++sLrPtWvXEBkZiSFDhmDZsmUYPXo0AHa0FhAQgHnz5mHMmDG8zzU9oktKSkL16tVx//59eHl5FTVMRUlJSUG1atUQExMDT09PqcMRndp/foB+BwD9DtT+8wPsDF9gYCCePXsGb2/vYj23WKcup0yZguHDh1vdJyQkBI8ePQJgfE3O1dUVISEhuH//vsXnurq6wtXV1Wy7l5eXav9x83l6eqr6d6D2nx+g3wFAvwO1//wA4OBQ/MkCxUp0fn5+8PPzK3S/Fi1awNXVFdevX0f79u0BADk5OYiOjkb16tWLHSQhhBBSUoIMRvH09MTYsWMxa9YsVKtWDdWrV8dXX30FABgwYIAQb0kIIYTwEmwe3VdffQUnJycMGzYMGRkZCA0Nxf79++Hj41Pk13B1dcWsWbN4T2eqhdp/B2r/+QH6HQD0O1D7zw+U7ndQrMEohBBCiNxQrUtCCCGKRomOEEKIolGiI4QQomiU6AghhCiarBIdtf1hsrKy0LRpU2g0Gpw/f17qcEQTHR2NkSNHIjg4GO7u7qhRowZmzZqF7OxsqUMTzI8//oigoCC4ubkhNDQUp06dkjok0YSHh6NVq1bw8PCAv78/+vfvj+vXr0sdlmQWLlwIjUaDSZMmSR2KqGJjYzF06FD4+vrC3d0djRo1wpkzZ4r1GrJJdBs3bsSwYcMwYsQIXLhwAceOHcPgwYOlDksSH3/8MapUqSJ1GKKLioqCTqfDsmXLcOXKFXz33XdYunQppk+fLnVogli/fj0mT56MWbNmITIyEk2aNEGPHj2QkJAgdWiiOHToEMaPH4+IiAjs2bMHOTk56N69O9LT06UOTXSnT5/GsmXL0LhxY6lDEdWzZ8/Qrl07ODs7Y8eOHbh69Sq++eabYk1TAwBBijrbWk5ODle1alXu559/ljoUyW3fvp2rW7cud+XKFQ4Ad+7cOalDktSXX37JBQcHSx2GIFq3bs2NHz9ev67VarkqVapw4eHhEkYlnYSEBA4Ad+jQIalDEVVqaipXq1Ytbs+ePVynTp24iRMnSh2SaD755BOuffv2pX4dWRzRmbb9qVy5Mnr16qW6Rq7x8fEYNWoUVq9ejTJlykgdjl1ITk5G+fLlpQ7D5rKzs3H27FmEhYXptzk4OCAsLAwnTpyQMDLp5LftUuK/tzXjx49Hnz59jP4W1OLff/9Fy5YtMWDAAPj7+6NZs2ZYsWJFsV9HFonuzp07AIDZs2djxowZ2Lp1K3x8fNC5c2c8ffpU4ujEwXEchg8fjrFjx6Jly5ZSh2MXbt26hcWLF1vshiFnT548gVarRcWKFY22V6xYEXFxcRJFJR2dTodJkyahXbt2VntaKs26desQGRmJ8PBwqUORxJ07d7BkyRLUqlULu3btwrhx4/D+++9j1apVxXodSRPd1KlTodForN7yr8sAwKefforXXnsNLVq0wG+//QaNRoMNGzZI+SOUWlF/B4sXL0ZqaiqmTZsmdcg2V9TfQUGxsbHo2bMnBgwYgFGjRkkUORHL+PHjcfnyZaxbt07qUEQTExODiRMnYs2aNXBzc5M6HEnodDo0b94cCxYsQLNmzTB69GiMGjUKS5cuLdbrCFbrsiiEbvsjB0X9Hezfvx8nTpwwq/PWsmVLDBkypNjfcOxJUX8H+R4+fIguXbqgbdu2WL58ucDRSaNChQpwdHREfHy80fb4+HhUqlRJoqikMWHCBGzduhWHDx9GQECA1OGI5uzZs0hISEDz5s3127RaLQ4fPowffvgBWVlZcHR0lDBC4VWuXNnocx8A6tWrh40bNxbrdSRNdNT2p+i/g0WLFmHevHn69YcPH6JHjx5Yv349QkNDhQxRcEX9HQDsSK5Lly76o/qS9KaSAxcXF7Ro0QL79u3TT6PR6XTYt28fJkyYIG1wIuE4Du+99x42b96MgwcPIjg4WOqQRNWtWzdcunTJaNuIESNQt25dfPLJJ4pPcgDQrl07syklN27cKP7nfqmHs4hk4sSJXNWqVbldu3ZxUVFR3MiRIzl/f3/u6dOnUocmibt376pu1OWDBw+4mjVrct26deMePHjAPXr0SH9TonXr1nGurq7cypUruatXr3KjR4/mvL29ubi4OKlDE8W4ceM4Ly8v7uDBg0b/1s+fP5c6NMmobdTlqVOnOCcnJ27+/PnczZs3uTVr1nBlypTh/vjjj2K9jmwSXXZ2NjdlyhTO39+f8/Dw4MLCwrjLly9LHZZk1JjofvvtNw4A702pFi9ezAUGBnIuLi5c69atuYiICKlDEo2lf+vffvtN6tAko7ZEx3Ec999//3ENGzbkXF1dubp163LLly8v9mtQmx5CCCGKpswLHIQQQkgeSnSEEEIUjRIdIYQQRaNERwghRNEo0RFCCFE0SnSEEEIUjRIdIYQQRaNERwghRNEo0RFCCFE0SnSEEEIUjRIdIYQQRaNERwghRNH+H2VFGUIpO0WRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.set_xlim([-6,6])\n",
    "ax.set_ylim([-6,6])\n",
    "plt.plot(x[0], y[0]);\n",
    "plt.plot(x[1], y[1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see in the above image, the comet 67P had a rather strong encounter with Jupiter a few years ago. Of course, if you wanted to do a realistic simulation of that encounter, you'd need to include all the other planets and maybe even some non-gravitational effects for the comet. However, let's stick with our simplistic model and try to find out when exactly the two bodies had a close encounter. We already stored the data, so we can just plot their distance as a function of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum distance (0.047401 AU) occured at time: -63.790379 years.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.set_xlabel(\"time [yrs]\")\n",
    "ax.set_ylabel(\"distance [AU]\")\n",
    "distance = np.sqrt(np.square(x[0]-x[1])+np.square(y[0]-y[1])+np.square(z[0]-z[1]))\n",
    "plt.plot(times/year, distance);\n",
    "closeencountertime = times[np.argmin(distance)]/year\n",
    "print(\"Minimum distance (%f AU) occured at time: %f years.\" % (np.min(distance),closeencountertime))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the minimum distance occured approximately 56 years ago (as of writing this tutorial). Let's see what date that was using some python magic and the datetime module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1959-02-04 08:09'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import datetime\n",
    "encounterdate = datetime.datetime.today() + datetime.timedelta(days=365.25*closeencountertime)\n",
    "encounterdate.strftime(\"%Y-%m-%d %H:%M\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you check [Wikipedia](https://en.wikipedia.org/wiki/67P/Churyumov–Gerasimenko) or [JPL](https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=67P;old=0;orb=0;cov=0;log=0;cad=1#cad), the encounter happened on 1959-Feb-04 06:24, so we are not far off (it turns out that's because of jets and other non-gravitational forces from the comet!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
